commit e39a9fec53d62544b6dcad47d190cfeb54f52da7 Author: Adog64 Date: Thu Feb 22 14:22:36 2024 -0500 6th Semester Files diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-01/Aliasing.png b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/Aliasing.png new file mode 100644 index 0000000..42e00f8 Binary files /dev/null and b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/Aliasing.png differ diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-01/DTFT1.png b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/DTFT1.png new file mode 100644 index 0000000..8b9abd8 Binary files /dev/null and b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/DTFT1.png differ diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-01/DiminishingReturns.png b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/DiminishingReturns.png new file mode 100644 index 0000000..00214c6 Binary files /dev/null and b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/DiminishingReturns.png differ diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-01/LoFreqSampling.png 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diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-01/dsp-lab-01.pdf b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/dsp-lab-01.pdf new file mode 100644 index 0000000..3a97981 Binary files /dev/null and b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/dsp-lab-01.pdf differ diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-01/dsp-lab-01.synctex.gz b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/dsp-lab-01.synctex.gz new file mode 100644 index 0000000..d75b619 Binary files /dev/null and b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/dsp-lab-01.synctex.gz differ diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-01/dsp-lab-01.tex b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/dsp-lab-01.tex new file mode 100644 index 0000000..145e7f3 --- /dev/null +++ b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/dsp-lab-01.tex @@ -0,0 +1,86 @@ +\documentclass{IEEEtran}[journal] + +\usepackage{amsmath} +\usepackage{graphicx} +\usepackage{listings} + +\title{Exploring the Sampling Theorem with Fourier Analysis} +\author{Aidan Sharpe \& Elise Heim} + +\DeclareMathOperator{\sinc}{sinc} + +\begin{document} +\maketitle + +\section{Results and Discussion} +\subsection{Aliasing} +The sampling theorem states that the sampling frequency must be at least twice the maximum frequency in a signal to be able to uniquely identify each frequency in the signal. When this condition, called the \emph{Nyquist sampling rate condition} is not satisfied, frequencies are no longer distinct. For example, given a sampling frequency of 100[Hz], the maximum distinct frequency is 50[Hz]. Seen in figure \ref{fig:aliasing}, despite being two frequencies: 20[Hz] (top) and 80[Hz] (bottom), they appear the same when plotted. + +\begin{figure}[h] + \includegraphics[width=0.48\textwidth]{Aliasing.png} + \caption{Ambiguous frequency between 20[Hz] and 80[Hz]} + \label{fig:aliasing} +\end{figure} + +Applying the discrete Fourier transform on the samples of the 20[Hz] signal reveals large frequency contributions at 20[Hz] and 80[Hz] as seen in figure \ref{fig:20HzDTFT}. +\begin{figure}[h] + \includegraphics[width=0.48\textwidth]{DTFT1.png} + \caption{Discrete Time Fourier Transform of 20[Hz] signal sampled at 100[Hz]} + \label{fig:20HzDTFT} +\end{figure} +Even though the signal is strictly a 20[Hz] sinusoidal signal, there seems to be a very strong contribution of 80[Hz]. The correct interpretation of this information is that the samples are identical for an 80[Hz] signal and a 20[Hz] signal sampled at 100[Hz]. + +\subsection{Fourier Analysis of the Difference of Two Unit Steps} + +The Fourier transform is a powerful tool that can convert any signal in the time domain to a corresponding representation in the frequency domain. Given a signal, $x(t)$, its Fourier transform is given by: +\begin{equation} + X(\omega) = F[x(t)] = \int\limits_{-\infty}^{\infty} x(t)e^{-j\omega t} dt + \label{eqn:fourier} +\end{equation} +where $\omega$ is the angular frequency. Consider the difference of two unit steps: +$$x(t) = u(t+1/2) - u(t-1/2)$$ +In this case, $x(t)$ only impacts the region in which the integral is not zero, so rather than taking the difference of two unit step integrals, the bounds of integration can simply be reduced to $[-1/2, 1/2]$. Evaluating this simpler integral gives: +\begin{equation} + F[u(t+1/2) - u(t-1/2)] = {2 \sin(\omega/2) \over \omega} +\end{equation} +This result can be verified by using the \verb|fourier(x)| function in MATLAB\textsuperscript{\tiny\textregistered}. In this case, there is no maximum frequency since the Fourier transform is periodic. Therefore, the signal is not band-limited, and lossless sampling is not possible. By sampling with higher frequency, higher fidelity can be achieved. However, since the contribution of frequencies is inversely proportional to the frequency, there will quickly be diminishing returns with high frequency sampling. + +Using a MATLAB\textsuperscript{\tiny\textregistered} script to calculate the percent of the power provided by the first $k$ periods of the Fourier transform of $x(t)$, the diminishing returns are quantified and plotted in figure \ref{fig:diminish}. +\begin{figure}[h] + \includegraphics[width=0.48\textwidth]{DiminishingReturns.png} + \caption{Diminishing returns on higher fidelity sampling} + \label{fig:diminish} +\end{figure} + +\subsection{Fourier Analysis of the $\sinc(t)$ Function} +Using the definition of the Fourier transform in equation \ref{eqn:fourier}, the $\sinc(t)$ function can be derived to be: +\begin{equation} +F[\sinc(t)] = \pi u(\pi-\omega) - \pi u(-\pi-\omega) +\end{equation} +where $\sinc(t)$ is the normalized sinc function, and $u(\omega)$ is the unit step. The normalized sinc function was chosen over the unnormalized variant because it is more widely used in telecommunications and signal processing. + +\subsection{Sampling Low Frequency Signals} +Considering the signal, $x_\text{compound}(t) = \cos(2\pi t / 5) + \sin(4\pi t / 7) + \cos(16\pi t / 9)$, the maximum frequency is less than 2[Hz]. Therefore, a sampling frequency of only 4[Hz] would still satisfy he Nyquist sampling rate condition. Seen in figure \ref{fig:lofreq} are the first 100 samples of a 4[Hz] sampling of $x_\text{compound}(t)$. +\begin{figure}[h] + \includegraphics[width=0.48\textwidth]{LoFreqSampling.png} + \caption{First 100 samples of $x_\text{compound}(t)$ at a sampling rate of 4[Hz]} + \label{fig:lofreq} +\end{figure} + +While the samples may appear quite random, by taking the discrete Fourier transform, and plotting the sums of the corresponding sinusoidal signals, the original continuous time signal can be recovered. + +\subsection{Symbolic Fourier Analysis in MATLAB\textsuperscript{\tiny\textregistered}} +Finding the Fourier transform of $x(t) = e^{-4t} u(t)$ can be accomplished by evaluating the integral in equation \ref{eqn:fourier}. This results in the answer of $\frac{1}{4+j\omega}$. MATLAB\textsuperscript{\tiny\textregistered} can be utilized to confirm these calculations with the assistance of a very short program. + +In order to find the Fourier transform of the function $x(t) = {\mathrm{e}}^{-a\,\left|t\right|}$, one must begin by taking the integral +\begin{equation} + X(\omega) = \int e^{-a|t|}e^{-j\omega t}dt +\end{equation} +where $a$ is a constant. Evaluating yields two terms: +$${1 \over a + j\omega} + {1 \over a - j\omega}$$ +These terms can further be combined and simplified to $\frac{2\,a}{a^2 +w^2 }$. These calculations were confirmed through a short MATLAB program that resulted in the same answer. Another MATLAB program can be utilized to find the Fourier transform of $x(t) = \cos \left(b\,t\right)$. This result is $\pi \,{\left({\delta }\left(b+w\right)+{\delta }\left(b-w\right)\right)}$. + +\subsection{Two-Dimensional Sampling} +In one dimension, we can consider sampling a time signal. In higher dimensions, we have a continuous-valued function. We evaluate this signal at intervals measured in meters. There are two types of frequencies: continuous space frequency associated with the original image, and discrete space frequency. The Fourier representations for continuous space signals and sampled discrete space signals are important for understanding sampling. The discrete space frequency is equal to the continuous space frequency multiplied by the sampling interval, and the discrete space is equal to continuous space times the sampling interval. The sampling frequencies are similar to the one-dimensional case, where a sample continuous space signal is the sum of samples multiplied by impulses. The spectrum is proportional to the convolution of the original signal and the Fourier transform. The spacing is inversely proportional because they were originally spaced in the frequency domain. Convolution with impulses shifts the function closer to zero, resulting in a sample signal spectrum proportional to the original signal spectrum shifted. The original signal spectrum is represented by a two-dimensional frequency domain quantity, replicated at the sampling frequencies. To prevent aliasing, the bandwidth must be smaller than half of the spacing between these replicas. The two-dimensional version of the Nyquist Sampling Theorem states that if the original image is band-limited, then it can be uniquely constructed from the samples taken. This requires achieving the same sample in a set time. A reconstruction can be created by taking a low-pass filter in two dimensions and choosing the portion of the spectrum that corresponds to the first term of the replicated sample signal spectrum. + +\end{document} diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-01/lab1q1.m b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/lab1q1.m new file mode 100644 index 0000000..0c003bc --- /dev/null +++ b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/lab1q1.m @@ -0,0 +1,11 @@ +fs = 100; +t = [0:1/fs:1/fs * 10]; +f1 = 80; +f2 = 20; +x1 = cos(2*pi*f1*t); +x2 = cos(2*pi*f2*t); + +subplot(2,1,1); +plot(t,x1); +subplot(2,1,2); +plot(t,x2); \ No newline at end of file diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-01/lab1q1.py b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/lab1q1.py new file mode 100644 index 0000000..bed365d --- /dev/null +++ b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/lab1q1.py @@ -0,0 +1,19 @@ +from matplotlib import pyplot as plt +import numpy as np + +PI = np.pi + +fs = 100 +t = np.arange(0, 100/fs, 1/fs) + +f2 = 80 +f1 = 40 + +x1 = np.cos(2*PI*f1*t) +x2 = np.cos(2*PI*f2*t) + +x = np.cos(2*PI*t/7) + np.sin(4*PI*t/7) + np.cos(16*PI*t/9) + +plt.plot(np.arange(0,fs), abs(np.fft.fft(x1*x2))) + +plt.show() diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-01/lab1q2.m b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/lab1q2.m new file mode 100644 index 0000000..4595444 --- /dev/null +++ b/6th-Semester-Spring-2024/DSP/Labs/Lab-01/lab1q2.m @@ -0,0 +1,13 @@ +syms W +for k=1:24; + E(k)=single(int((sin(0.5*W)/(0.5*W))^2 ,W,0,k*pi)/pi); +end +stem(E,'linewidth',2); +hold on +EE=0.9900*ones(1,24); +plot(EE,'r','linewidth',2) +set(gca,'XTick',0:5:25) +set(gca,'XTickLabel',{'0','5\pi','10\pi','15\pi','20\pi','25\pi'}) +xlabel('Angular frequency') +ylabel('Signal Energy') +axis([0 25 0 1.1]) diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-02/dsp-lab-02.aux b/6th-Semester-Spring-2024/DSP/Labs/Lab-02/dsp-lab-02.aux new file mode 100644 index 0000000..22f9773 --- /dev/null +++ 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+\usepackage{graphicx} +\usepackage{listings} + +\title{} +\author{Aidan Sharpe \& Elise Heim} + +\DeclareMathOperator{\sinc}{sinc} + +\begin{document} +\maketitle + +\begin{abstract} +\end{abstract} + +\section{Introduction} + +\section{Results \& Discussion} +\subsection{Analysis of Amplitude Modulation} +A message, $m(t)$, with a bandwidth, $B=2[\text{kHz}]$ modulates a cosine carrier with a frequency of 10[kHz]. The combined signal is $s(t) = m(t)\cos(20000\pi t)$. Using a Fourier transform on $s(t)$ reveals a maximum frequency at 12[kHz]. In fact, as seen in figure \ref{fig:AM_Fourier_Whitenoise}, by filling the band that $m(t)$ occupies with white noise, the Fourier transform of $s(t)$ contains white noise centered on the carrier frequency with twice the bandwidth of the original signal. The spike that occurs at 10[kHz] is the result of the original signal having a DC term and the carrier frequency having a value of 10[kHz]. + +\begin{figure}[h] + \includegraphics[width=0.48\textwidth]{lab2_1a.png} + \caption{The Fourier transform of a white noise signal carried at 10[kHz]} + \label{fig:AM_Fourier_Whitenoise} +\end{figure} + +If instead, $m(t)$ had a triangular spectrum of amplitude 1, the spectrum of $s(t)$ will be two triangles touching at the base at 10[kHz] as seen in figure \ref{fig:carried_triangle}. + +\begin{figure}[h] + \includegraphics[width=0.48\textwidth]{lab2_1b.png} + \caption{The Fourier transform of a signal with a triangular spectrum carried at 10[kHz]} + \label{fig:carried_triangle} +\end{figure} + +\subsection{Periodicity and Sampling Frequency} +Consider the signal $x(t) = \cos(2\pi t/7)$. Given the standard forms, $\cos(2\pi f t)$ and $\cos(\omega t)$, where f is linear frequency and $\omega$ is angular frequency, $f = {1\over7}$ and $\omega = {2\pi \over 7}$. Given a sampling frequency of 1[Hz], the sampling theorem is satisfied. To determine if a sampled signal is periodic, the condition $\omega N = 2 \pi r$, where $r$ is the smallest integer such that $N$ is an integer, must be satisfied. + + + + +\section{Conclusions} + +\end{document} diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-02/lab-02-1.py b/6th-Semester-Spring-2024/DSP/Labs/Lab-02/lab-02-1.py new file mode 100644 index 0000000..7446e1a --- /dev/null +++ b/6th-Semester-Spring-2024/DSP/Labs/Lab-02/lab-02-1.py @@ -0,0 +1,22 @@ +import numpy as np +import matplotlib.pyplot as plt + +PI = np.pi + + +fs = 20000 +t = np.arange(0, 1, 1/fs) + +fB = np.arange(0,2001,1) +fC = 10000 + +m = np.zeros_like(t) +for f in fB: + m += np.cos(2*PI*f*t)*(-abs(f-1000)/1000 + 1) + +c = np.cos(2*PI*fC*t) +s = m*c + +plt.plot(np.arange(0,fs), abs(np.fft.fft(s))) + +plt.show() diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-02/lab-02-2.py b/6th-Semester-Spring-2024/DSP/Labs/Lab-02/lab-02-2.py new file mode 100644 index 0000000..1882099 --- /dev/null +++ b/6th-Semester-Spring-2024/DSP/Labs/Lab-02/lab-02-2.py @@ -0,0 +1,14 @@ +import numpy as np +import matplotlib.pyplot as plt + +PI = np.pi + + +fs = 20000 +t = np.arange(0, 1, 1/fs) + +x = np.cos(2*PI*t/7) + +plt.plot(np.arange(0,fs), abs(np.fft.fft(s))) + +plt.show() diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-02/lab-02-5.py b/6th-Semester-Spring-2024/DSP/Labs/Lab-02/lab-02-5.py new file mode 100644 index 0000000..475a415 --- /dev/null +++ b/6th-Semester-Spring-2024/DSP/Labs/Lab-02/lab-02-5.py @@ -0,0 +1,23 @@ +import numpy as np +import matplotlib.pyplot as plt + +def x(n): + return (1/n) * np.heaviside(n, 0.5) + +n = np.arange(1,100) + +y = x(n) + +E_x_total = 0 +E_x = np.zeros(len(y)) + +for i in range(len(y)): + E_x_total += abs(y[i])**2 + E_x[i] = E_x_total + +fig, ax = plt.subplots() +ax.scatter(n,y, label="x[n]") +ax.scatter(n, E_x, c='red', label="E_x") +ax.axhline(np.pi**2 / 6, linestyle='-') +ax.legend() +plt.show() diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-02/lab2_1a.png b/6th-Semester-Spring-2024/DSP/Labs/Lab-02/lab2_1a.png new file mode 100644 index 0000000..d342f72 Binary files /dev/null and b/6th-Semester-Spring-2024/DSP/Labs/Lab-02/lab2_1a.png differ diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-02/lab2_1b.png b/6th-Semester-Spring-2024/DSP/Labs/Lab-02/lab2_1b.png new file mode 100644 index 0000000..f7ddf5b Binary files /dev/null and b/6th-Semester-Spring-2024/DSP/Labs/Lab-02/lab2_1b.png differ diff --git a/6th-Semester-Spring-2024/DSP/Notes/citations.bib b/6th-Semester-Spring-2024/DSP/Notes/citations.bib new file mode 100644 index 0000000..c6994b8 --- /dev/null +++ b/6th-Semester-Spring-2024/DSP/Notes/citations.bib @@ -0,0 +1,8 @@ +@misc{xie2021symmetric, + title={On Symmetric Invertible Binary Pairing Functions}, + author={Jianrui Xie}, + year={2021}, + eprint={2105.10752}, + archivePrefix={arXiv}, + primaryClass={math.CO} +} diff --git a/6th-Semester-Spring-2024/DSP/Notes/dsp-notes.aux 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b/6th-Semester-Spring-2024/DSP/Notes/dsp-notes.synctex.gz new file mode 100644 index 0000000..5030b05 Binary files /dev/null and b/6th-Semester-Spring-2024/DSP/Notes/dsp-notes.synctex.gz differ diff --git a/6th-Semester-Spring-2024/DSP/Notes/dsp-notes.tex b/6th-Semester-Spring-2024/DSP/Notes/dsp-notes.tex new file mode 100644 index 0000000..d53cade --- /dev/null +++ b/6th-Semester-Spring-2024/DSP/Notes/dsp-notes.tex @@ -0,0 +1,646 @@ +\documentclass{report} + +\input{preamble} +\input{macros} +\input{letterfonts} + +\title{\Huge{Digital Signal Processing}} +\author{\huge{Aidan Sharpe}} +\date{} + +\begin{document} + +\maketitle +\newpage% or \cleardoublepage +% \pdfbookmark[]{}{<dest>} +\pdfbookmark[section]{\contentsname}{toc} +\tableofcontents +\pagebreak + + +A signal is anything that is used to convey information. Analog signals are continuously variable, but in this course the focus will be put on digital signals. Digital signals are signals that are made up of discrete values. Some advantages of using digital signals are as follows: +\begin{enumerate} + \item Flexibility and programmibility + \item More immune to noise + \item Signal reproducibility + \item Ease of maintenance and troubleshooting + \item Signal storage +\end{enumerate} + +Furthermore, a signal can depend on any number of variables. A signal that only depends on one variable is considered \emph{one-dimensional}. This course will primarily be directed towards these one-dimensional signals. + +One example of the many use cases for digital signal processing is speech processing. This can include another range of topics such as speech recognition, speech enhancement, and speech encoding and compression. + +\chapter{Discrete Time Signals} + +\section{Uniform Sampling} +The first step to uniform sampling is to discretize the time axis. Uniform sampling converts a continuous time signal, $x(t)$ into a discrete signal by considering the samples of $x(t)$ at uniform times, $t=nT_s$; where $n$ is an integer and $T_s$ is the sampling period. +\\ +\\ +The Dirac Delta function, or the impulse function is defined as: +$$\delta(t) = \begin{cases} + 0 & t < 0 \\ + \infty & t = 0 \\ + 0 & t > 0 +\end{cases}$$ +The strength of the impulse function is typically defined to be unity. This is more rigorously given by: +$$\int\limits_{-\infty}^\infty \delta(t) dt = 1$$ +The sampling property of the impulse function is defined as: +$$f(t)\delta(t-t_0) = f(t_0)\delta(t-t_0)$$ +The sifting property of the impulse function is given by: +$$\int\limits_{-\infty}^{\infty} f(t)\delta(t-t_0) dt = f(t_0)$$ +To sample a signal, $x(t)$, uniformly through time, an impulse train is used. Each sample of the signal can be written in the form: +$$x(t)\delta(t - nT_s)$$ +Therefore, the resulting sampled signal at all times, $t$, is given by: +$$x_s(t) = x(t)\sum_{n=-\infty}^\infty \delta(t - nT_s)$$ +The signal, $x_\text{imp}(t)$, is a continuous and periodic function with period, $T_s$. It is given by: +$$x_\text{imp}(t) = \sum_{n=-\infty}^\infty \delta(t - nT_s)$$ +Since the definition of the Fourier series states that any continuous and periodic signal can be represented as a linear weighted combination of complex exponentials, we can rewrite $x_\text{imp}(t)$ in terms of a complex Fourier series: +$$x_\text{imp}(t) = \sum_{k = -\infty}^\infty X_k e^{jk\Omega_s t}$$ +Where: +\begin{itemize} + \item[$X_k$] are the Fourier series coefficients + \item[$\Omega_s$] is the angular sampling frequency defined as $\Omega_s = {2\pi \over T_s}$ +\end{itemize} +Since $\Omega_s$ is entirely dependent on $T_s$, the only unknown is the values of the Fourier series coefficients, $X_k$. These coefficients can be found by: +$$X_k = {1\over T_s} \int\limits_{-T_s \over 2}^{T_s \over 2} \delta(t) e^{-jk\Omega_s t} dt$$ +In this case, $X_k$ is always $1 \over T_s$. Therefore, the Fourier series definition for $x_\text{imp}(t)$ is: +$$x_\text{imp}(t) = \sum_{k=-\infty}^\infty {1 \over T_s} e^{jk\Omega_s t}$$ +To sample $x(t)$ and get $x_s(t)$, simply take the product of $x(t)$ and $x_\text{imp}(t)$: +$$x_s(t) = \sum_{k = -\infty}^\infty {1 \over T_s} x(t) e^{jk\Omega_s t}$$ +This sampled signal is called a discrete signal or a digital signal. While working with $x_s(t)$ in this form is not often practical, taking a Fourier transform gives more insight. +$$F[\delta(t - a)] = e^{-j\Omega a}$$ +$$x(t) \xleftrightarrow{F} X(\Omega)$$ +$$x(t - \alpha) \xleftrightarrow{F} X(\Omega)e^{-j\Omega\alpha}$$ +$$x(t)e^{jn\Omega_0 t} \xleftrightarrow{F} = X(\Omega - \Omega_0)$$ +Using these properties, the Fourier transform of $x_s(t)$ is: +$$F[x_s(t)] = F\lt[{1\over T_s} \sum_{n = -\infty}^{\infty} x(t)e^{jn\Omega_s t}\rt]$$ +$$X_s(\Omega) = {1\over T_s} \sum_{n=-\infty}^\infty F\lt[x(t) e^{jn\Omega_s t}\rt]$$ +$$X_s(\Omega) = {1\over T_s} \sum_{n=-\infty}^\infty X(\Omega - n\Omega_s)$$ +$$X_s(\Omega) = {1\over T_s} X(\Omega)$$ + +\thm{The Sampling Theorem} +{ + A band-limited signal, $x(t)$---its low-pass spectrum $X(\Omega)$ is such that $X(\Omega) = 0$ for $|\Omega| > \Omega_\text{max}$ where $\Omega_\text{max}$ is the maximum frequency in $x(t)$---can be sampled uniformly and without frequency aliasing (overlap between spectral copies) using a sampling frequency of $\Omega_s = {2\pi \over T_s} \ge 2\Omega$ called the Nyquist sampling rate condition. +} + +\ex{Sampling Theorem} +{ + A signal, $x(t)$, is given by: + $$x(t) = 2\cos(2\pi t + {\pi \over 4})$$ + Since there exists a maximum frequency, in this case, 1[Hz], $x(t)$ is considered a band-limited signal. + $$f_s \ge 2f_m$$ + $$f_s \ge 2\text{[Hz]}$$ + $$T_s \le {1\over 2}\lt[\text{samples/s}\rt]$$ +} + +A good figure of merit is to let $\Omega_\text{max}$ be the frequency such that 99\% of the signal energy is in the interval $[-\Omega_\text{max}, \Omega_\text{max}]$. The signal energy in the time domain is given by: +$$E_x = \int\limits_{-\infty}^\infty |x(t)|^2 dt$$ +Using the Perseval's relationship, the signal energy can be computed using only knowledge from the frequency domain. +$$E_x = {1\over 2\pi} \int\limits_{-\infty}^\infty |X(\omega)|^2 dt$$ + +\section{Characterizing Discrete Signals in the Time Domain} +\dfn{Causal Signal} +{ + $x[n]$ is said to be a \emph{causal signal} if $x[n]$ has zero value for $n < 0$. +} +\noindent +When a signal, $x[n]$, is discritized following the sampling theorem, it domain is the integers, and it can take real and complex values. + +\dfn{Anti-Causal Signal} +{ + $x[n]$ is said to be an \emph{anti-causal signal} if $x[n]$ has zero value for $n \ge 0$. +} +\noindent +At $n=0$, a causal signal can have a nonzero value, but an anti-causal signal cannot. + +\dfn{Finite Support Signal} +{ + $x[n]$ is said to have \emph{finite support} if there exists integers, $N_1$ and $N_2$, such that $x[n]$ has zero value for $n < N_1$ and $N_2$, where $N_2 \le N_1$. +} + +\noindent +Finite support signals have a finite domain, and for discrete signals, finite values of $n$ that correspond to a non-zero signal value. + +\dfn{Infinite Support Signals} +{ + $x[n]$ is said to have \emph{infinite support} or infinite duration if it does not have finite support. +} + +\noindent +For infinite support signals, there do not exist two integers, $N_1$ and $N_2$, such that $x[n] = 0$ for $n < N_1$ and $n > N_2$. Infinite support signals exist in the following forms: +\begin{enumerate} + \item Right-sided signal: $N < n < \infty$ + \item Left-sided signal: $-\infty < n < N$ + \item Two-sided signal: $-\infty < n < \infty$ +\end{enumerate} + +\dfn{Discrete Impulse} +{ + The impulse signal can be written in the discrete domain as: + $$\delta[n] = \begin{cases} + 1 & n=0 \\ + 0 & \text{otherwise} + \end{cases}$$ +} + +\noindent +Since the discrete impulse signal has a non-zero value only at $n=1$, it is a causal signal with finite support. + +\ex{} +{ + Consider the signal, $x[n] = \delta[n - a]$: + $$\delta[n-a] = \begin{cases} + 0 & n < a \\ + 1 & n = a \\ + 0 & n > a \\ + \end{cases}$$ + + Since $x[n]$ has a non-zero value only at $n = a$, it is a finite support signal. If $a \ge 0$, the signal is causal, but if $a < 0$, the signal is non-causal. In this case, if $a < 0$, then it is also an anti-causal signal. +} + +\noindent +Any finite support signal can be represented in terms of discrete impulses. +$$x[n] = \sum_{a = N_1}^{N_2} k_a \delta[n - a]$$ + +\dfn{Discrete Unit Step} +{ + The \emph{discrete unit step}, $u[n]$ is defined as: + $$u[n] = \begin{cases} + 1 & n \ge 0 \\ + 0 & \text{otherwise} + \end{cases}$$ +} + +\noindent +The discrete unit step has right-sided infinite support and is a causal signal. The signal, $u[-n]$ is defined as: +$$u[-n] = \begin{cases} + 1 & n \le 0 \\ + 0 & \text{otherwise} +\end{cases}$$ +$u[-n]$ has left-sided infinite support, but it is neither causal nor anti-causal. + +\section{The Norm of a Discrete Signal} + +\dfn{Norm of a Discrete Signal} +{ + The mapping of a signal to a value in the range, $[0, \infty)$. +} + +\dfn{The $L_p$ Norm} +{ + Given a discrete time signal, $x[n]$, the $L_p$ norm of the signal is: + $$\lt[\sum_n |x[n]|^p \rt]^{1/p}$$ +} + +\ex{$L_p$ Norm} +{ + $$x[n] = \begin{bmatrix}3 & -5 & 7 & -5 & -9\end{bmatrix}$$ + Find the $L_1$, $L_2$, and $L_\infty$ norms: + \\ + \\ + $L_1$ norm: + $$\sum_n |x[n]| = 3 + 5 + 7 + 5 + 9 = 29$$ + $L_2$ norm: + $$\lt[\sum_n |x[n]|^2 \rt]^{1/2} = sqrt{9 + 25 + 49 + 25 + 81} = \sqrt{189} = 3\sqrt{21}$$ + $L_\infty$ norm: + $$\max|x[n]| = 9$$ +} + +\ex{$L_p$ Norms with Complex Numbers} +{ + $$x[n] = \begin{bmatrix}3+j & -5+j3 & -7-j & 9-j4 & 10\end{bmatrix}$$ + \\ + \\ + $L_1$ norm: + $$\sum_n |x[n]| = \sqrt{10} + sqrt{34} + \sqrt{50} + \sqrt{97} + 10$$ + $L_2$ norm: + $$\lt[\sum_n |x[n]|^2 \rt]^{1/2} = \sqrt{10 + 34 + 50 + 97 + 100}$$ + $L_\infty$ norm: + $$\max|x[n]| = 10$$ +} + +\ex{} +{ + $$x[n] = \begin{bmatrix}1 & j & 1 & j & 1 & j & 1 & j & \cdots\end{bmatrix}, n \in \mathbb{Z} \cap [0, 99]$$ + \\ + \\ + $L_1$ norm: + $$\sum_n |x[n]| = 100$$ + $L_2$ norm: + $$\lt[\sum_n |x[n]|^2 \rt]^{1/2} = \sqrt{100} = 10$$ + $L_\infty$ norm: + $$\max|x[n]| = 1$$ +} + +\subsection{Geometric Series} +There are two types of geometric series: finite and infinite. +\dfn{Infinite Geometric Series} +{ + Infinite geometric series are of the form: + $$\sum_{n=m}^{\infty} s^n = {s^m \over 1 - s}$$ + If $|s| < 1$, the series will converge, and if $|s| > 1$, the series will diverge. +} + +\dfn{Finite Geometric Series} +{ + A finite geometric series is of the form: + $$\sum_{n=0}^{N-1} s^n$$ + If $s = 1$, the series converges to $N$, otherwise the series can be evaluated by: + $$\sum_{n=0}^{N-1} s^n = {1 - s^N \over 1 - s}$$ +} + +\ex{Norms of Geometric Series} +{ + $$x[n] = (-0.5)^n u[n]$$ + \\ + \\ + $L_1$ norm: + $$\sum_n |x[n]| = \sum_{n=0}^\infty |(-0.5)^n| = \sum_{n=0}^\infty {1\over2}^n = 2$$ + $L_2$ norm: + $$\lt[ \sum_n |x[n]|^2 \rt]^{1/2} = \lt[ \sum_{n=0}^\infty |(-0.5)^n|^2 \rt]^{1/2} = \lt[ \sum_{n=0}^\infty {1\over4}^n \rt]^{1/2} = \lt({1\over 1 - 0.25}\rt)^{1/2} = \sqrt{4\over3}$$ + $L_\infty$ norm: + $$\max|x[n]| = \max(0.5^n), n \in \mathbb{N}_0 = 1$$ +} +\noindent +For geometric series, if $s < 1$, the $L_\infty$ norm will occur at the smallest $n$ in the series.Conversely, for geometric series where $s > 1$, the $L_\infty$ norm will occur at the largest $n$ in the series. + +\section{Elementary Operations on Signals} +An elementary operation operates on each element of a signal. Consider two signals, $x[n]$ and $h[n]$. Assume that the two signals are sampled at the same frequency. + +\begin{center} + \begin{tabular}{c | c | c | c | c | c} + $n$ & $x[n]$ & $h[n]$ & $x[n] + h[n]$ & $x[n] - h[n]$ & $x[n]h[n]$\\ + \hline + -2 & 3 & & 3 & 3 & 0\\ + -1 & -5 & -7 & -12 & 2 & 35\\ + 0 & 2 & 3 & 5 & -1 & 6\\ + 1 & -6 & 10 & 4 & -16 & -60\\ + 2 & 9 & 21 & 30 & -12 & 289 \\ + 3 & & -16 & -16 & 16 & 0\\ + 4 & & 6 & 6 & -6 & 0\\ + 5 & & -3 & -3 & 3 & 0 + \end{tabular} +\end{center} + +\noindent +In addition to these element-by-element arithmetic operations, elementary operations may also manipulate the input space. +\\ +\\ +\noindent +A signal may be time delayed by $a$ in the form $h[n - a]$. Signals can be advanced by $a$ in the form $h[n + a]$. Time may also be reflected around $n=0$ in the form $h[-n]$. Perhaps the most interesting operation is the circular shift. + +\dfn{Circular Shift} +{ + The circular shift is a time shifting operation on a finite length sequence that results in another sequence of the same length and defined for the same range of values of $n$. The domain of the signal will be unchanged. +} +\noindent +The modulus operation: +$$r = m\bmod N = \langle m \rangle_N$$ + +\noindent +Another type of discrete elementary operation is the signal rate operation. This involves adding or removing samples. + +\dfn{The Downsample Operation} +{ + The downsample or sub-sample operation on a signal, $x[n]$ is given by: + $$y[n] = x[Mn], M \in \mathbb{Z}$$ + This downsamples from every $n$ to every $M^\text{th}$ sample from $x[n]$ +} +\noindent +When downsampling, the sampling frequency $f_s$ becomes $f_s \over M$, and the sampling time, $T_s$ becomes $M T_s$. + +\nt +{ + To avoid aliasing, $f_s \overset{!}{\ge} 2f_m$. Beware that downsampling may cause aliasing by decreasing $f_s$ too much. +} + +\noindent +On the other hand, a signal may also be upsampled. +\dfn{The Upsample Operation} +{ + Sampling frequency increases by a factor of $M$. + $$y[n] = x\lt[{n \over M}\rt], M \in \mathbb{Z}$$ + This will insert $M-1$ zeros between successive samples of $x[n]$. +} + +\ex{Upsampling} +{ + $$x[n] = \begin{bmatrix} 1 & 2 & 3 & 4 \end{bmatrix}$$ + $$M = 4$$ + $$y[n] = \begin{bmatrix} 1 & 0 & 0 & 0 & 2 & \cdots & 4 \end{bmatrix}$$ +} + +\noindent +When upsampling, the sampling frequency, $f_s$ becomes $Mf_s$, and the sampling time, $T_s$ becomes $T_s \over M$. + +\chapter{Discrete Systems} +A discrete system is any system that takes a discrete signal as input and produces a discrete signal as output. + +$$x[n] \to \boxed{S} \to y[n]$$ + +\section{Properties of Systems} +\subsection{Linearity} +For a system to be considered linear, it must satisfy two conditions: homogeneity and superposition. +\subsubsection{Homogeneity} +For a system to be homogeneous, a scaling of the input by a constant, $a$, must produce an output scaled by that same constant, $a$. +$$y[n] = S[x[n]$$ +$$ay[n] = S[ax[n]]$$ + +\subsubsection{Superposition} +For a system to satisfy superposition, taking the sum of two inputs $x_1[n]$ and $x_2[n]$ as input must produce the sum of their individual outputs $y_1[n] + y_2[n]$. +$$y_1[n] = S[x_1[n]]$$ +$$y_2[n] = S[x_2[n]]$$ +$$y_1[n] + y_2[n] = S[x_1[n] + x_2[n]]$$ + +\subsection{Time Invarience} +For a system to be considered time invariant, delaying or advancing the input must lead to the same delay or advance in the output. +$$y[n] = S[x[n]$$ +$$y[n-a] = S[x[n-a]]$$ + +\subsection{Causality} +For a system to be considered causal, the output must only rely on past and present inputs; it cannot depend on any future inputs. + +\subsection{Bounded Input, Bounded Output (BIBO) Stability} +A system is BIBO stable if every bounded input has a corresponding bounded output. +\\ +\\ +\noindent +A bounded input is of the form: +$$\lt|x[n]\rt| \le B_x < \infty, \forall n$$ +A bounded output is of the form: +$$\lt|y[n]\rt| \le B_y < \infty, \forall n$$ + +\nt +{ + For unbounded inputs, outputs do not have to be bounded. +} + +\ex{Properties of Downsampling} +{ + The definition of the downsampling operation: + $$y[n] = S[x[n]] = x[Mn]$$ + \subsubsection{Homogeneity} + $$S[a x[n]] = a x[M n]$$ + $$s y[n] = a x[M n] \to \text{The system is homogeneous.}$$ + + \subsubsection{Superposition} + $$y_1[n] = S[x_1[n]] = x_1[M n]$$ + $$y_2[n] = S[x_2[n]] = x_2[M n]$$ + $$S[x_1[n] + x_2[n]] = x_1[M n] + x_2[M n] = y_1[n] + y_2[n] \to \text{Superposition holds.}$$ + + \subsubsection{Time Invariance} + $$S[x[n-a] = x[Mn-a]$$ + $$y[n - a] = x[M(n-a)] = X[Mn - Ma] \ne S[x[n-a]] \to \text{The system is not time invariant}$$ + + \subsubsection{Causality} + For any value of $M$ greater than $1$, and $n$ greater than $1$, $Mn$ will always be greater than $n$, therefore relying on future inputs. + + \subsubsection{BIBO Stability} + If $|x[n]|$ is bounded by $B_x$ for all $n$, then the output is bounded by $B_y = B_x$ for all $n$. + +} + +\section{LTI Systems} +Linear and time-invariant (LTI) systems are simple systems that are very useful for modelling. + +\dfn{Impulse Response} +{ + The output of a system when the Dirac delta (impulse) function is applied as input. +} +\noindent +For discrete systems, the impulse response is given by $h[n]$ as opposed to the $h(t)$ for continuous systems. + +\paragraph{Properties of the Discrete LTI Systems} +\begin{enumerate} + \item The system is causal if the umpulse response is a causal signal + \item The system is BIBO stable if the impulse response is absolutely stable + $$\sum_n |h[n]| < \infty$$ + \item $y[n]$ is computeable for any $x[n]$ +\end{enumerate} + +\subsubsection{The Integral Test} +Given a continuous, positive, and decreasing function in the interval $[1, \infty)$, the indefinite integral and sum either both converge or both diverge. + +\subsubsection{Convolution} +If the input to the LTI system is $x[n]$ and the impulse response of the LTI system is $h[n]$, the convolution of $x[n]$ and $h[n]$ is given by: +$$y[n] = x[n] * h[n]$$ +In the continuous case, the convolution of $x(t)$ and $h(t)$ is given by: +$$y(t) = x(t) * h(t) = \int\limits_{-\infty}^\infty x(\tau)h(t-\tau)d\tau$$ +In the discrete case, the convolution of $x[n]$ and $h[n]$ is given by: +$$y[n] = x[n] * h[n] = \sum_{k=-\infty}^\infty x[k]h[n-k] = \sum_{k=-\infty}^\infty h[k]x[n-k]$$ + +\section{Periodicity} +A periodic continuous signal with period $T$ is given by: +$$x(t) = x(t - kT)$$ +A periodic discrete signal with integer period $N$ is given by: +$$x[n] = x(t - kN)$$ +The period of a discrete signal must be an integer because discrete signals are only defined at integer intervals. +\\ +\\ +\noindent +If two discrete signals, $x[t]$ and $y[t]$ are periodic with periods $N_1$ and $N_2$, the period of the sum of the signals is the least common multiple of $N_1$ and $N_2$. If even one signal in a sum of signals is aperiodic, then the entire sum becomes aperiodic. +\\ +\\ +\noindent +In the continuous time domain, sinusoidal and complex exponential signals are always periodic. For discrete signals, however, it is not as simple. A cosine in the discrete domain takes the form: +$$x[n] = \cos(\omega_0 n + \varphi)$$ +By the definition of periodicity, for $x[n]$ to be periodic with period $N$: +$$x[n] = x[n+N] = \cos(\omega_0(n+N) + \varphi)$$ +By distributing $\omega_0$ and applying a trigonometric identity: +$$x[n+N] = \cos(\omega_0 n + \varphi)\cos(\omega_0 N) - \sin(\omega_0 n + \varphi)\cos(\omega_0 N)$$ +Therefore, for $x[n]$ to equal $x[n+N]$, the sine terms must go to 0 and $\cos(\omega_0 N)$ must be unity. If $\omega_0$ is an integer multiple of $2\pi$, this condition will be satisfied. + +\ex{Periodic Sampling} +{ + Given a signal $\cos(\pi n)$, what is it's corresponding integer period? + $$\omega_0 = \pi$$ + $$\omega_0 N = 2\pi r$$ + $$\pi N = 2\pi r$$ + $$N = 2r$$ + The smallest integer $r$ resulting in an integer $N$ is $r=1$. For $r=1$, $N=2$, therefore the signal is periodic with $N=2$. +} + +\ex{Aperiodic Sampling} +{ + Given the signal $\cos(e\pi n + {7\pi /9})$ find it's corresponding integer period. + $$\omega_0 = e \pi$$ + $$\omega_0 N = 2\pi r$$ + $$e\pi N = 2 \pi r$$ + $$N = {2 \over e} r$$ + There is no integer $r$ such that $N$ is an integer. Therefore the original signal is not discretely periodic. + +} + +\section{Energy and Power} +\subsection{Energy} +For a continuous signal, $x(t)$, the total energy is given by: +$$E_x = \int\limits_{-\infty}^{\infty} |x(t)|^2 dt$$ +Similarly, for a discrete time signal, the total energy is given by: +$$E_x = \sum_n |x[n]|^2$$ +which is the same as the square of the L-2 norm of $x[n]$. +\subsection{Power} +The power of a signal is calculated slightly differently for periodic and aperiodic signals. For discrete, periodic signals with period, $N$, the power is given by: +$$P_x = {1\over N} \sum_{n=0}^{N-1} |x[n]|^2$$ +For aperiodic discrete signals, the power is given by: +$$P_x = \lim_{k\to\infty} {1 \over 2k + 1} \sum_{n=-k}^{k} |x[n]|^2$$ +\nt +{ + Periodic signals have infinite energy and finite power, while aperiodic signals with finite energy have zero power. +} + +\ex{} +{ + Given $[x] = 3(-1)^n u[n]$ compute the energy and power. Since $x[n]=0$ for $n<0$, the signal is aperiodic. + $$E_x = \sum_n |x[n]|^2$$ + $$E_x = \sum_{n=0}^{\infty} |3(-1)^n|^2$$ + $$E_x = \sum_{n=0}^{\infty} 9 \rightarrow \infty$$ + Given that the signal is aperiodic, the power is given by: + $$P_x = \lim_{k\to\infty} {1 \over 2k + 1} \sum_{n=-k}^{k} |x[n]|^2$$ + $$P_x = \lim_{k\to\infty} {1 \over 2k + 1} \sum_{n=0}^{k} 9$$ + $$P_x = \lim_{k\to\infty} {1 \over 2k + 1} 9(k+1)$$ + $$P_x = \lim_{k\to\infty} {9(k+1) \over 2k + 1} 9(k+1)$$ + By L'hopital's rule, + $$P_x = \lim_{k\to\infty} {9\over2} = {9 \over 2}$$ +} + +\chapter{} + +\section{The Discrete Time Fourier Transform} +\subsection{Derivation of the Discrete Time Fourier Transform} +Consider the signal $x_s(t)$ given by: +$$x_s(t) = \sum_{n = -\infty}^\infty x(t) \delta(t - nT_s)$$ +Apply a Fourier transform: +$$F\lt[x_s(t)\rt] = F\lt[\sum_{n=-\infty}^\infty x(t) \delta(t-nT_s)\rt]$$ +By the sampling property of the impulse, $x(t)\delta(t-nT_s)$ becomes $x(nT_s)\delta(t-nT_s)$. +$$F\lt[x_s(t)\rt] = F\lt[\sum_{n=-\infty}^\infty x(nT_s) \delta(t-nT_s)\rt]$$ +The sum and $x(t)$ may be taken out of the Fourier transform: +$$F\lt[x_s(t)\rt] = \sum_{n=-\infty}^\infty x(nT_s) F\big[\delta(t-nT_s)\big]$$ +The Fourier transform of the impulse is unity, and the delay by $nT_s$ becomes a complex exponential: +$$X_s(\Omega) = \sum_{n=-\infty}^\infty x[nT_s]e^{-j\Omega n T_s}$$ +If $T_s$ is unity, then simplification is possible. Converting $x[nT_s]$ to $x[n]$ yields the discrete time Fourier transform: +$$X(e^{-j\omega}) = \sum_{n=-\infty}^\infty x[n]e^{-j\omega n}$$ + +\nt +{ + $\Omega$ is the continuous angular frequency while $\omega$ is the discrete angular frequency. + $$\Omega T_s = \omega$$ +} +\noindent +This is a natural extension of the continuous Fourier transform: +$$X(\Omega) = \int\limits_{-\infty}^{\infty}x(t)e^{-\Omega t}dt$$ +$X(e^{j\omega}$ is periodic with a period of $2\pi$. + +\dfn{Discrete Time Fourier Transform} +{ + $$X(e^{j\omega}) = \sum_{n=-\infty}^\infty x[n]e^{-j\omega n}$$ +} + +\ex{DTFT of the Impulse} +{ + Consider $x[n] = \delta[n]$. Find the DTFT of $x[n]$. + + $$X(e^{j\omega}) = \sum_{n=-\infty}^\infty x[n]e^{-j\omega n}$$ + $$X(e^{j\omega}) = \sum_{n=-\infty}^\infty \delta[n]e^{-j\omega n}$$ + The expression in the sum has a non-zero value only at $n=0$, therefore the sum only has one term. + $$X(e^{j\omega}) = e^{-j\omega (0)} = 1$$ +} + +\ex{More Complicated DTFT} +{ + Consider $x[n] = a^n u[n]$. Find the DTFT of $x[n]$. + $$X(e^{j\omega}) = \sum_{n=-\infty}^\infty x[n]e^{-j\omega n}$$ + Since $u[n]$ only has a non-zero value for $n\ge0$, the sum can be simplified to: + $$X(e^{j\omega}) = \sum_{n=0}^\infty a^n e^{-j\omega n}$$ + Since both terms in the sum have $n$ in the exponent: + $$X(e^{j\omega}) = \sum_{n=0}^\infty (a e^{-j\omega})^n$$ + The sum has the form of a geometric series, which can be evaluated by: + $$\sum_{n=m}^{\infty} = {s^m \over 1-s}, |s| < 1$$ + Since $|e^{-j\omega}| = 1$, $|s| = |a|$. Therefore: + $$F\lt[a^n u[n]\rt] = {1 \over 1 - ae^{-j\omega}}, |a| < 1$$ +} + +\subsection{Properties of the Discrete Time Fourier Transform} +\begin{enumerate} + \item The DTFT is a linear operation. + \item If a signal is delayed or advanced ($x[n-a]$), the DTFT is scaled by $e^{-j\omega a}$. + \item The DTFT of $nx[n]$ is $j{d\over d\omega}(X(e^{j\omega}))$ + \item The DTFT of the convolution, $x[n] * h[n]$, is the same as the product of the DTFT of the two signals. +\end{enumerate} + +\ex{Time Multiplication Property} +{ + Consider $x[n] = na^nu[n]$. Find the DTFT of $x[n]$. + Since the DTFT of $a^nu[n]$ is known to be${1 \over 1 - ae^{-j\omega}}$, by the time multiplication property of the DTFT, the DTFT of $x[n]$ is: + $$X(e^{j\omega}) = j{d \over d\omega} \lt[{1 \over 1 - ae^{-j\omega}}\rt]$$ +} + +\nt +{ + If $x[n]$ is absolutely summable ($\sum|x[n]| < \infty$) then the DTFT exists. +} + +\subsection{Special Cases} +In some special cases, the DTFT exists, but the corresponding time domain signal is not absolutely summable. +\ex{Ideal Lowpass Filter} +{ + Consider the transfer function of an ideal lowpass filter, with cutoff frequency, $\omega_c$. +} + +\chapter{The Z-Transform} +Recall the Laplace transform is defined as: +$$X(s) = \int_{-\infty}^\infty x(t) e^{-st}dt$$ +where $s$ is a complex variable. The analogous transform in the discrete domain is called the Z-transform, which is given by: +$$X(z) = \sum_n x[n]z^{-n}$$ +where $z$ is a complex variable. The region of convergence of a Z-transform is the set of all $z$ for which the sum converges. +\ex{Z-Transform of causal finite support signals} +{ + Given a causal, finite support signal, $x[n] = \begin{bmatrix}a&b&c&d\end{bmatrix}, 0 \le n \le 3$. Find its $z$ transform. + + $$X(z) = \sum_{n=0}^3 x[n] z^{-n}$$ + $$X(z) = a + bz^{-1} + cz^{-2} + dz^{-3}$$ + The region of convergence is all values of $z$ except $z=0$. +} + +\ex{Z-Transform of anti-causal finite support signals} +{ + Given the finite support, anti-causal signal, $x[n] = \begin{bmatrix}a&b&c&d\end{bmatrix}, -4\le n \le -1$. + $$X(z) = \sum_{n=-4}^{-1} x[n] z^{-n}$$ + $$X(z) = az^4 + bz^4 + cz^2 + dz$$ + The region of convergence is all values of $z$ except $z=\infty$. +} + +\ex{Z-Transform of causal nor anti-causal signals} +{ + Given the finite support signal, $x[n] = \begin{bmatrix}a&b&c&d\end{bmatrix}, -2\le n\le 1$. + $$X(z) = \sum_{n=-2}^1 x[n] z^{-n}$$ + $$X(z) = az^2 + bz + c + dz^{-1}$$ + The region of convergence is all $z$ except $z=0$ and $z=\infty$ +} +\noindent +For finite support, discrete signals, the region of convergence is always the entire $z$-plane with the possible exception of $z=0$ and $z=\infty$. +\ex{Z-Transform of the discrete unit impulse} +{ + Given $x[n] = \delta[n]$: + $$X(z) = \sum_n = \delta[n]z^{-n}$$ + $$X(z) = 1$$ + The region of convergence is the entire $z$ plane. +} +\ex{Z-Transform of infinite support signals} +{ + Given the infinite support signal, $x[n] = a^n u[n]$: + $$X(z) = \sum_{n=0}^\infty a^nz^{-n}$$ + The common exponent, $n$ can be taken out to put it in the form: + $$\sum_{n=m}^\infty s^n = {s^m \over 1 -s}$$ + where $s=a z^{-1}$ in this case. This sum will converge as long as $|a z^{-1}| < 1$. In simpler terms, the sum will converge when $|z| > |a|$. +} +\noindent +Since $z$ is a complex variable, it can be described in a polar form: +$$z = re^{j\theta}$$ +where $r$ is the magnitude and $\theta$ is the phase angle. +\\ +\\ +\noindent +If a region of convergence (ROC) does not include the unit circle, then its DTFT does not exist except for special case signals. If the ROC \emph{does} contain the unit circle, then the DTFT can be found by substituting $z = e^{j\omega}$. + +\end{document} diff --git a/6th-Semester-Spring-2024/DSP/Notes/dsp-notes.toc b/6th-Semester-Spring-2024/DSP/Notes/dsp-notes.toc new file mode 100644 index 0000000..3a2109e --- /dev/null +++ b/6th-Semester-Spring-2024/DSP/Notes/dsp-notes.toc @@ -0,0 +1,34 @@ +\contentsline {chapter}{\numberline {1}Discrete Time Signals}{3}{chapter.1}% +\contentsline {section}{\numberline {1.1}Uniform Sampling}{3}{section.1.1}% +\contentsline {section}{\numberline {1.2}Characterizing Discrete Signals in the Time Domain}{5}{section.1.2}% +\contentsline {section}{\numberline {1.3}The Norm of a Discrete Signal}{6}{section.1.3}% +\contentsline {subsection}{\numberline {1.3.1}Geometric Series}{8}{subsection.1.3.1}% +\contentsline {section}{\numberline {1.4}Elementary Operations on Signals}{9}{section.1.4}% +\contentsline {chapter}{\numberline {2}Discrete Systems}{11}{chapter.2}% +\contentsline {section}{\numberline {2.1}Properties of Systems}{11}{section.2.1}% +\contentsline {subsection}{\numberline {2.1.1}Linearity}{11}{subsection.2.1.1}% +\contentsline {subsubsection}{Homogeneity}{11}{section*.2}% +\contentsline {subsubsection}{Superposition}{11}{section*.3}% +\contentsline {subsection}{\numberline {2.1.2}Time Invarience}{11}{subsection.2.1.2}% +\contentsline {subsection}{\numberline {2.1.3}Causality}{11}{subsection.2.1.3}% +\contentsline {subsection}{\numberline {2.1.4}Bounded Input, Bounded Output (BIBO) Stability}{12}{subsection.2.1.4}% +\contentsline {subsubsection}{Homogeneity}{12}{section*.4}% +\contentsline {subsubsection}{Superposition}{12}{section*.5}% +\contentsline {subsubsection}{Time Invariance}{12}{section*.6}% +\contentsline {subsubsection}{Causality}{12}{section*.7}% +\contentsline {subsubsection}{BIBO Stability}{12}{section*.8}% +\contentsline {section}{\numberline {2.2}LTI Systems}{12}{section.2.2}% +\contentsline {paragraph}{Properties of the Discrete LTI Systems}{12}{section*.9}% +\contentsline {subsubsection}{The Integral Test}{13}{section*.10}% +\contentsline {subsubsection}{Convolution}{13}{section*.11}% +\contentsline {section}{\numberline {2.3}Periodicity}{13}{section.2.3}% +\contentsline {section}{\numberline {2.4}Energy and Power}{14}{section.2.4}% +\contentsline {subsection}{\numberline {2.4.1}Energy}{14}{subsection.2.4.1}% +\contentsline {subsection}{\numberline {2.4.2}Power}{14}{subsection.2.4.2}% +\contentsline {chapter}{\numberline {3}}{16}{chapter.3}% +\contentsline {section}{\numberline {3.1}The Discrete Time Fourier Transform}{16}{section.3.1}% +\contentsline {subsection}{\numberline {3.1.1}Derivation of the Discrete Time Fourier Transform}{16}{subsection.3.1.1}% +\contentsline {subsection}{\numberline {3.1.2}Properties of the Discrete Time Fourier Transform}{17}{subsection.3.1.2}% +\contentsline {subsection}{\numberline {3.1.3}Special Cases}{18}{subsection.3.1.3}% +\contentsline {chapter}{\numberline {4}The Z-Transform}{19}{chapter.4}% +\contentsfinish diff --git a/6th-Semester-Spring-2024/DSP/Notes/letterfonts.tex b/6th-Semester-Spring-2024/DSP/Notes/letterfonts.tex new file mode 100644 index 0000000..e28675f --- /dev/null +++ b/6th-Semester-Spring-2024/DSP/Notes/letterfonts.tex @@ -0,0 +1,178 @@ +% Things Lie +\newcommand{\kb}{\mathfrak b} +\newcommand{\kg}{\mathfrak g} +\newcommand{\kh}{\mathfrak h} +\newcommand{\kn}{\mathfrak n} +\newcommand{\ku}{\mathfrak u} +\newcommand{\kz}{\mathfrak z} +\DeclareMathOperator{\Ext}{Ext} % Ext functor +\DeclareMathOperator{\Tor}{Tor} % Tor functor +\newcommand{\gl}{\opname{\mathfrak{gl}}} % frak gl group +\renewcommand{\sl}{\opname{\mathfrak{sl}}} % frak sl group chktex 6 + +% More script letters etc. +\newcommand{\SA}{\mathcal A} +\newcommand{\SB}{\mathcal B} +\newcommand{\SC}{\mathcal C} +\newcommand{\SF}{\mathcal F} +\newcommand{\SG}{\mathcal G} +\newcommand{\SH}{\mathcal H} +\newcommand{\OO}{\mathcal O} + +\newcommand{\SCA}{\mathscr A} +\newcommand{\SCB}{\mathscr B} +\newcommand{\SCC}{\mathscr C} +\newcommand{\SCD}{\mathscr D} +\newcommand{\SCE}{\mathscr E} +\newcommand{\SCF}{\mathscr F} +\newcommand{\SCG}{\mathscr G} +\newcommand{\SCH}{\mathscr H} + +% Mathfrak primes +\newcommand{\km}{\mathfrak m} +\newcommand{\kp}{\mathfrak p} +\newcommand{\kq}{\mathfrak q} + +% number sets +\newcommand{\RR}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{R}}{\mathbb{R}^{#1}}}} +\newcommand{\NN}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{N}}{\mathbb{N}^{#1}}}} +\newcommand{\ZZ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Z}}{\mathbb{Z}^{#1}}}} +\newcommand{\QQ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Q}}{\mathbb{Q}^{#1}}}} +\newcommand{\CC}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{C}}{\mathbb{C}^{#1}}}} +\newcommand{\PP}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{P}}{\mathbb{P}^{#1}}}} +\newcommand{\HH}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{H}}{\mathbb{H}^{#1}}}} +\newcommand{\FF}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{F}}{\mathbb{F}^{#1}}}} +% expected value +\newcommand{\EE}{\ensuremath{\mathbb{E}}} +\newcommand{\charin}{\text{ char }} +\DeclareMathOperator{\sign}{sign} +\DeclareMathOperator{\Aut}{Aut} +\DeclareMathOperator{\Inn}{Inn} +\DeclareMathOperator{\Syl}{Syl} +\DeclareMathOperator{\Gal}{Gal} +\DeclareMathOperator{\GL}{GL} % General linear group +\DeclareMathOperator{\SL}{SL} % Special linear group + +%--------------------------------------- +% BlackBoard Math Fonts :- +%--------------------------------------- + +%Captital Letters +\newcommand{\bbA}{\mathbb{A}} \newcommand{\bbB}{\mathbb{B}} +\newcommand{\bbC}{\mathbb{C}} \newcommand{\bbD}{\mathbb{D}} +\newcommand{\bbE}{\mathbb{E}} \newcommand{\bbF}{\mathbb{F}} +\newcommand{\bbG}{\mathbb{G}} \newcommand{\bbH}{\mathbb{H}} +\newcommand{\bbI}{\mathbb{I}} \newcommand{\bbJ}{\mathbb{J}} +\newcommand{\bbK}{\mathbb{K}} \newcommand{\bbL}{\mathbb{L}} +\newcommand{\bbM}{\mathbb{M}} \newcommand{\bbN}{\mathbb{N}} +\newcommand{\bbO}{\mathbb{O}} \newcommand{\bbP}{\mathbb{P}} +\newcommand{\bbQ}{\mathbb{Q}} \newcommand{\bbR}{\mathbb{R}} +\newcommand{\bbS}{\mathbb{S}} \newcommand{\bbT}{\mathbb{T}} +\newcommand{\bbU}{\mathbb{U}} \newcommand{\bbV}{\mathbb{V}} +\newcommand{\bbW}{\mathbb{W}} \newcommand{\bbX}{\mathbb{X}} +\newcommand{\bbY}{\mathbb{Y}} \newcommand{\bbZ}{\mathbb{Z}} + +%--------------------------------------- +% MathCal Fonts :- +%--------------------------------------- + +%Captital Letters +\newcommand{\mcA}{\mathcal{A}} \newcommand{\mcB}{\mathcal{B}} +\newcommand{\mcC}{\mathcal{C}} \newcommand{\mcD}{\mathcal{D}} +\newcommand{\mcE}{\mathcal{E}} \newcommand{\mcF}{\mathcal{F}} +\newcommand{\mcG}{\mathcal{G}} \newcommand{\mcH}{\mathcal{H}} +\newcommand{\mcI}{\mathcal{I}} \newcommand{\mcJ}{\mathcal{J}} +\newcommand{\mcK}{\mathcal{K}} \newcommand{\mcL}{\mathcal{L}} +\newcommand{\mcM}{\mathcal{M}} \newcommand{\mcN}{\mathcal{N}} +\newcommand{\mcO}{\mathcal{O}} \newcommand{\mcP}{\mathcal{P}} +\newcommand{\mcQ}{\mathcal{Q}} \newcommand{\mcR}{\mathcal{R}} +\newcommand{\mcS}{\mathcal{S}} \newcommand{\mcT}{\mathcal{T}} +\newcommand{\mcU}{\mathcal{U}} \newcommand{\mcV}{\mathcal{V}} +\newcommand{\mcW}{\mathcal{W}} \newcommand{\mcX}{\mathcal{X}} +\newcommand{\mcY}{\mathcal{Y}} \newcommand{\mcZ}{\mathcal{Z}} + + +%--------------------------------------- +% Bold Math Fonts :- +%--------------------------------------- + +%Captital Letters +\newcommand{\bmA}{\boldsymbol{A}} \newcommand{\bmB}{\boldsymbol{B}} +\newcommand{\bmC}{\boldsymbol{C}} \newcommand{\bmD}{\boldsymbol{D}} +\newcommand{\bmE}{\boldsymbol{E}} \newcommand{\bmF}{\boldsymbol{F}} +\newcommand{\bmG}{\boldsymbol{G}} \newcommand{\bmH}{\boldsymbol{H}} +\newcommand{\bmI}{\boldsymbol{I}} \newcommand{\bmJ}{\boldsymbol{J}} +\newcommand{\bmK}{\boldsymbol{K}} \newcommand{\bmL}{\boldsymbol{L}} +\newcommand{\bmM}{\boldsymbol{M}} \newcommand{\bmN}{\boldsymbol{N}} +\newcommand{\bmO}{\boldsymbol{O}} \newcommand{\bmP}{\boldsymbol{P}} +\newcommand{\bmQ}{\boldsymbol{Q}} \newcommand{\bmR}{\boldsymbol{R}} +\newcommand{\bmS}{\boldsymbol{S}} \newcommand{\bmT}{\boldsymbol{T}} +\newcommand{\bmU}{\boldsymbol{U}} \newcommand{\bmV}{\boldsymbol{V}} +\newcommand{\bmW}{\boldsymbol{W}} \newcommand{\bmX}{\boldsymbol{X}} +\newcommand{\bmY}{\boldsymbol{Y}} \newcommand{\bmZ}{\boldsymbol{Z}} +%Small Letters +\newcommand{\bma}{\boldsymbol{a}} \newcommand{\bmb}{\boldsymbol{b}} +\newcommand{\bmc}{\boldsymbol{c}} \newcommand{\bmd}{\boldsymbol{d}} +\newcommand{\bme}{\boldsymbol{e}} \newcommand{\bmf}{\boldsymbol{f}} +\newcommand{\bmg}{\boldsymbol{g}} \newcommand{\bmh}{\boldsymbol{h}} +\newcommand{\bmi}{\boldsymbol{i}} \newcommand{\bmj}{\boldsymbol{j}} +\newcommand{\bmk}{\boldsymbol{k}} \newcommand{\bml}{\boldsymbol{l}} +\newcommand{\bmm}{\boldsymbol{m}} \newcommand{\bmn}{\boldsymbol{n}} +\newcommand{\bmo}{\boldsymbol{o}} \newcommand{\bmp}{\boldsymbol{p}} +\newcommand{\bmq}{\boldsymbol{q}} \newcommand{\bmr}{\boldsymbol{r}} +\newcommand{\bms}{\boldsymbol{s}} \newcommand{\bmt}{\boldsymbol{t}} +\newcommand{\bmu}{\boldsymbol{u}} \newcommand{\bmv}{\boldsymbol{v}} +\newcommand{\bmw}{\boldsymbol{w}} \newcommand{\bmx}{\boldsymbol{x}} +\newcommand{\bmy}{\boldsymbol{y}} \newcommand{\bmz}{\boldsymbol{z}} + +%--------------------------------------- +% Scr Math Fonts :- +%--------------------------------------- + +\newcommand{\sA}{{\mathscr{A}}} \newcommand{\sB}{{\mathscr{B}}} +\newcommand{\sC}{{\mathscr{C}}} \newcommand{\sD}{{\mathscr{D}}} +\newcommand{\sE}{{\mathscr{E}}} \newcommand{\sF}{{\mathscr{F}}} +\newcommand{\sG}{{\mathscr{G}}} \newcommand{\sH}{{\mathscr{H}}} +\newcommand{\sI}{{\mathscr{I}}} \newcommand{\sJ}{{\mathscr{J}}} +\newcommand{\sK}{{\mathscr{K}}} \newcommand{\sL}{{\mathscr{L}}} +\newcommand{\sM}{{\mathscr{M}}} \newcommand{\sN}{{\mathscr{N}}} +\newcommand{\sO}{{\mathscr{O}}} \newcommand{\sP}{{\mathscr{P}}} +\newcommand{\sQ}{{\mathscr{Q}}} \newcommand{\sR}{{\mathscr{R}}} +\newcommand{\sS}{{\mathscr{S}}} \newcommand{\sT}{{\mathscr{T}}} +\newcommand{\sU}{{\mathscr{U}}} \newcommand{\sV}{{\mathscr{V}}} +\newcommand{\sW}{{\mathscr{W}}} \newcommand{\sX}{{\mathscr{X}}} +\newcommand{\sY}{{\mathscr{Y}}} \newcommand{\sZ}{{\mathscr{Z}}} + + +%--------------------------------------- +% Math Fraktur Font +%--------------------------------------- + +%Captital Letters +\newcommand{\mfA}{\mathfrak{A}} \newcommand{\mfB}{\mathfrak{B}} +\newcommand{\mfC}{\mathfrak{C}} \newcommand{\mfD}{\mathfrak{D}} +\newcommand{\mfE}{\mathfrak{E}} \newcommand{\mfF}{\mathfrak{F}} +\newcommand{\mfG}{\mathfrak{G}} \newcommand{\mfH}{\mathfrak{H}} +\newcommand{\mfI}{\mathfrak{I}} \newcommand{\mfJ}{\mathfrak{J}} +\newcommand{\mfK}{\mathfrak{K}} \newcommand{\mfL}{\mathfrak{L}} +\newcommand{\mfM}{\mathfrak{M}} \newcommand{\mfN}{\mathfrak{N}} +\newcommand{\mfO}{\mathfrak{O}} \newcommand{\mfP}{\mathfrak{P}} +\newcommand{\mfQ}{\mathfrak{Q}} \newcommand{\mfR}{\mathfrak{R}} +\newcommand{\mfS}{\mathfrak{S}} \newcommand{\mfT}{\mathfrak{T}} +\newcommand{\mfU}{\mathfrak{U}} \newcommand{\mfV}{\mathfrak{V}} +\newcommand{\mfW}{\mathfrak{W}} \newcommand{\mfX}{\mathfrak{X}} +\newcommand{\mfY}{\mathfrak{Y}} \newcommand{\mfZ}{\mathfrak{Z}} +%Small Letters +\newcommand{\mfa}{\mathfrak{a}} \newcommand{\mfb}{\mathfrak{b}} +\newcommand{\mfc}{\mathfrak{c}} \newcommand{\mfd}{\mathfrak{d}} +\newcommand{\mfe}{\mathfrak{e}} \newcommand{\mff}{\mathfrak{f}} +\newcommand{\mfg}{\mathfrak{g}} \newcommand{\mfh}{\mathfrak{h}} +\newcommand{\mfi}{\mathfrak{i}} \newcommand{\mfj}{\mathfrak{j}} +\newcommand{\mfk}{\mathfrak{k}} \newcommand{\mfl}{\mathfrak{l}} +\newcommand{\mfm}{\mathfrak{m}} \newcommand{\mfn}{\mathfrak{n}} +\newcommand{\mfo}{\mathfrak{o}} \newcommand{\mfp}{\mathfrak{p}} +\newcommand{\mfq}{\mathfrak{q}} \newcommand{\mfr}{\mathfrak{r}} +\newcommand{\mfs}{\mathfrak{s}} \newcommand{\mft}{\mathfrak{t}} +\newcommand{\mfu}{\mathfrak{u}} \newcommand{\mfv}{\mathfrak{v}} +\newcommand{\mfw}{\mathfrak{w}} \newcommand{\mfx}{\mathfrak{x}} +\newcommand{\mfy}{\mathfrak{y}} \newcommand{\mfz}{\mathfrak{z}} diff --git a/6th-Semester-Spring-2024/DSP/Notes/macros.tex b/6th-Semester-Spring-2024/DSP/Notes/macros.tex new file mode 100644 index 0000000..8bbdb96 --- /dev/null +++ b/6th-Semester-Spring-2024/DSP/Notes/macros.tex @@ -0,0 +1,88 @@ +%From M275 "Topology" at SJSU +\newcommand{\id}{\mathrm{id}} +\newcommand{\taking}[1]{\xrightarrow{#1}} +\newcommand{\inv}{^{-1}} + +%From M170 "Introduction to Graph Theory" at SJSU +\DeclareMathOperator{\diam}{diam} +\DeclareMathOperator{\ord}{ord} +\newcommand{\defeq}{\overset{\mathrm{def}}{=}} + +%From the USAMO .tex files +\newcommand{\ts}{\textsuperscript} +\newcommand{\dg}{^\circ} +\newcommand{\ii}{\item} + +% % From Math 55 and Math 145 at Harvard +% \newenvironment{subproof}[1][Proof]{% +% \begin{proof}[#1] \renewcommand{\qedsymbol}{$\blacksquare$}}% +% {\end{proof}} + +\newcommand{\liff}{\leftrightarrow} +\newcommand{\lthen}{\rightarrow} +\newcommand{\opname}{\operatorname} +\newcommand{\surjto}{\twoheadrightarrow} +\newcommand{\injto}{\hookrightarrow} +\newcommand{\On}{\mathrm{On}} % ordinals +\DeclareMathOperator{\img}{im} % Image +\DeclareMathOperator{\Img}{Im} % Image +\DeclareMathOperator{\coker}{coker} % Cokernel +\DeclareMathOperator{\Coker}{Coker} % Cokernel +\DeclareMathOperator{\Ker}{Ker} % Kernel +\DeclareMathOperator{\rank}{rank} +\DeclareMathOperator{\Spec}{Spec} % spectrum +\DeclareMathOperator{\Tr}{Tr} % trace +\DeclareMathOperator{\pr}{pr} % projection +\DeclareMathOperator{\ext}{ext} % extension +\DeclareMathOperator{\pred}{pred} % predecessor +\DeclareMathOperator{\dom}{dom} % domain +\DeclareMathOperator{\ran}{ran} % range +\DeclareMathOperator{\Hom}{Hom} % homomorphism +\DeclareMathOperator{\Mor}{Mor} % morphisms +\DeclareMathOperator{\End}{End} % endomorphism + +\newcommand{\eps}{\epsilon} +\newcommand{\veps}{\varepsilon} +\newcommand{\ol}{\overline} +\newcommand{\ul}{\underline} +\newcommand{\wt}{\widetilde} +\newcommand{\wh}{\widehat} +\newcommand{\vocab}[1]{\textbf{\color{blue} #1}} +\providecommand{\half}{\frac{1}{2}} +\newcommand{\dang}{\measuredangle} %% Directed angle +\newcommand{\ray}[1]{\overrightarrow{#1}} +\newcommand{\seg}[1]{\overline{#1}} +\newcommand{\arc}[1]{\wideparen{#1}} +\DeclareMathOperator{\cis}{cis} +\DeclareMathOperator*{\lcm}{lcm} +\DeclareMathOperator*{\argmin}{arg min} +\DeclareMathOperator*{\argmax}{arg max} +\newcommand{\cycsum}{\sum_{\mathrm{cyc}}} +\newcommand{\symsum}{\sum_{\mathrm{sym}}} +\newcommand{\cycprod}{\prod_{\mathrm{cyc}}} +\newcommand{\symprod}{\prod_{\mathrm{sym}}} +\newcommand{\Qed}{\begin{flushright}\qed\end{flushright}} +\newcommand{\parinn}{\setlength{\parindent}{1cm}} +\newcommand{\parinf}{\setlength{\parindent}{0cm}} +% \newcommand{\norm}{\|\cdot\|} +\newcommand{\inorm}{\norm_{\infty}} +\newcommand{\opensets}{\{V_{\alpha}\}_{\alpha\in I}} +\newcommand{\oset}{V_{\alpha}} +\newcommand{\opset}[1]{V_{\alpha_{#1}}} +\newcommand{\lub}{\text{lub}} +\newcommand{\del}[2]{\frac{\partial #1}{\partial #2}} +\newcommand{\Del}[3]{\frac{\partial^{#1} #2}{\partial^{#1} #3}} +\newcommand{\deld}[2]{\dfrac{\partial #1}{\partial #2}} +\newcommand{\Deld}[3]{\dfrac{\partial^{#1} #2}{\partial^{#1} #3}} +\newcommand{\lm}{\lambda} +\newcommand{\uin}{\mathbin{\rotatebox[origin=c]{90}{$\in$}}} +\newcommand{\usubset}{\mathbin{\rotatebox[origin=c]{90}{$\subset$}}} +\newcommand{\lt}{\left} +\newcommand{\rt}{\right} +\newcommand{\bs}[1]{\boldsymbol{#1}} +\newcommand{\exs}{\exists} +\newcommand{\st}{\strut} +\newcommand{\dps}[1]{\displaystyle{#1}} + +\newcommand{\sol}{\setlength{\parindent}{0cm}\textbf{\textit{Solution:}}\setlength{\parindent}{1cm} } +\newcommand{\solve}[1]{\setlength{\parindent}{0cm}\textbf{\textit{Solution: }}\setlength{\parindent}{1cm}#1 \Qed} diff --git a/6th-Semester-Spring-2024/DSP/Notes/preamble.tex b/6th-Semester-Spring-2024/DSP/Notes/preamble.tex new file mode 100644 index 0000000..af7d68e --- /dev/null +++ b/6th-Semester-Spring-2024/DSP/Notes/preamble.tex @@ -0,0 +1,779 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PACKAGE IMPORTS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\usepackage[tmargin=2cm,rmargin=1in,lmargin=1in,margin=0.85in,bmargin=2cm,footskip=.2in]{geometry} +\usepackage{amsmath,amsfonts,amsthm,amssymb,mathtools} +\usepackage{listings} +\usepackage[varbb]{newpxmath} +\usepackage{xfrac} +\usepackage[makeroom]{cancel} +\usepackage{mathtools} +\usepackage{bookmark} +\usepackage{enumitem} +\usepackage{hyperref,theoremref} +\hypersetup{ + pdftitle={Assignment}, + colorlinks=true, linkcolor=doc!90, + bookmarksnumbered=true, + bookmarksopen=true +} +\usepackage[most,many,breakable]{tcolorbox} +\usepackage{xcolor} +\usepackage{varwidth} +\usepackage{varwidth} +\usepackage{etoolbox} +%\usepackage{authblk} +\usepackage{nameref} +\usepackage{multicol,array} +\usepackage{tikz-cd} +\usepackage[ruled,vlined,linesnumbered]{algorithm2e} +\usepackage{comment} % enables the use of multi-line comments (\ifx \fi) +\usepackage{import} +\usepackage{xifthen} +\usepackage{pdfpages} +\usepackage{transparent} + +\newcommand\mycommfont[1]{\footnotesize\ttfamily\textcolor{blue}{#1}} +\SetCommentSty{mycommfont} +\newcommand{\incfig}[1]{% + \def\svgwidth{\columnwidth} + \import{./figures/}{#1.pdf_tex} +} + +\usepackage{tikzsymbols} +\renewcommand\qedsymbol{$\Laughey$} + + +%\usepackage{import} +%\usepackage{xifthen} +%\usepackage{pdfpages} +%\usepackage{transparent} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% SELF MADE COLORS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +\definecolor{myg}{RGB}{56, 140, 70} +\definecolor{myb}{RGB}{45, 111, 177} +\definecolor{myr}{RGB}{199, 68, 64} +\definecolor{mytheorembg}{HTML}{F2F2F9} +\definecolor{mytheoremfr}{HTML}{00007B} +\definecolor{mylenmabg}{HTML}{FFFAF8} +\definecolor{mylenmafr}{HTML}{983b0f} +\definecolor{mypropbg}{HTML}{f2fbfc} +\definecolor{mypropfr}{HTML}{191971} +\definecolor{myexamplebg}{HTML}{F2FBF8} +\definecolor{myexamplefr}{HTML}{88D6D1} +\definecolor{myexampleti}{HTML}{2A7F7F} +\definecolor{mydefinitbg}{HTML}{E5E5FF} +\definecolor{mydefinitfr}{HTML}{3F3FA3} +\definecolor{notesgreen}{RGB}{0,162,0} +\definecolor{myp}{RGB}{197, 92, 212} +\definecolor{mygr}{HTML}{2C3338} +\definecolor{myred}{RGB}{127,0,0} +\definecolor{myyellow}{RGB}{169,121,69} +\definecolor{myexercisebg}{HTML}{F2FBF8} +\definecolor{myexercisefg}{HTML}{88D6D1} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% TCOLORBOX SETUPS +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\setlength{\parindent}{1cm} +%================================ +% THEOREM BOX +%================================ + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{Theorem}{Theorem} +{% + enhanced, + breakable, + colback = mytheorembg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{mytheoremfr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mytheoremfr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mytheoremfr}, +} +{th} + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=chapter]{theorem}{Theorem} +{% + enhanced, + breakable, + colback = mytheorembg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{mytheoremfr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mytheoremfr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mytheoremfr}, +} +{th} + + +\tcbuselibrary{theorems,skins,hooks} +\newtcolorbox{Theoremcon} +{% + enhanced + ,breakable + ,colback = mytheorembg + ,frame hidden + ,boxrule = 0sp + ,borderline west = {2pt}{0pt}{mytheoremfr} + ,sharp corners + ,description font = \mdseries + ,separator sign none +} + +%================================ +% Corollery +%================================ +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{Corollary}{Corollary} +{% + enhanced + ,breakable + ,colback = myp!10 + ,frame hidden + ,boxrule = 0sp + ,borderline west = {2pt}{0pt}{myp!85!black} + ,sharp corners + ,detach title + ,before upper = \tcbtitle\par\smallskip + ,coltitle = myp!85!black + ,fonttitle = \bfseries\sffamily + ,description font = \mdseries + ,separator sign none + ,segmentation style={solid, myp!85!black} +} +{th} +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=chapter]{corollary}{Corollary} +{% + enhanced + ,breakable + ,colback = myp!10 + ,frame hidden + ,boxrule = 0sp + ,borderline west = {2pt}{0pt}{myp!85!black} + ,sharp corners + ,detach title + ,before upper = \tcbtitle\par\smallskip + ,coltitle = myp!85!black + ,fonttitle = \bfseries\sffamily + ,description font = \mdseries + ,separator sign none + ,segmentation style={solid, myp!85!black} +} +{th} + + +%================================ +% LENMA +%================================ + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{Review}{Review} +{% + enhanced, + breakable, + colback = mylenmabg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{mylenmafr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mylenmafr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mylenmafr}, +} +{th} + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=chapter]{review}{Review} +{% + enhanced, + breakable, + colback = mylenmabg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{mylenmafr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mylenmafr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mylenmafr}, +} +{th} + + +%================================ +% METHOD +%================================ + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{Method}{Method} +{% + enhanced, + breakable, + colback = mypropbg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{mypropfr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mypropfr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mypropfr}, +} +{th} + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=chapter]{method}{Method} +{% + enhanced, + breakable, + colback = mypropbg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{mypropfr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mypropfr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mypropfr}, +} +{th} + + +%================================ +% CLAIM +%================================ + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{claim}{Claim} +{% + enhanced + ,breakable + ,colback = myg!10 + ,frame hidden + ,boxrule = 0sp + ,borderline west = {2pt}{0pt}{myg} + ,sharp corners + ,detach title + ,before upper = \tcbtitle\par\smallskip + ,coltitle = myg!85!black + ,fonttitle = \bfseries\sffamily + ,description font = \mdseries + ,separator sign none + ,segmentation style={solid, myg!85!black} +} +{th} + + + +%================================ +% Exercise +%================================ + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{Exercise}{Exercise} +{% + enhanced, + breakable, + colback = myexercisebg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{myexercisefg}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = myexercisefg, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, myexercisefg}, +} +{th} + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=chapter]{exercise}{Exercise} +{% + enhanced, + breakable, + colback = myexercisebg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{myexercisefg}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = myexercisefg, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, myexercisefg}, +} +{th} + +%================================ +% EXAMPLE BOX +%================================ + +\newtcbtheorem[number within=section]{Example}{Example} +{% + colback = myexamplebg + ,breakable + ,colframe = myexamplefr + ,coltitle = myexampleti + ,boxrule = 1pt + ,sharp corners + ,detach title + ,before upper=\tcbtitle\par\smallskip + ,fonttitle = \bfseries + ,description font = \mdseries + ,separator sign none + ,description delimiters parenthesis +} +{ex} + +\newtcbtheorem[number within=chapter]{example}{Example} +{% + colback = myexamplebg + ,breakable + ,colframe = myexamplefr + ,coltitle = myexampleti + ,boxrule = 1pt + ,sharp corners + ,detach title + ,before upper=\tcbtitle\par\smallskip + ,fonttitle = \bfseries + ,description font = \mdseries + ,separator sign none + ,description delimiters parenthesis +} +{ex} + +%================================ +% DEFINITION BOX +%================================ + +\newtcbtheorem[number within=section]{Definition}{Definition}{enhanced, + before skip=2mm,after skip=2mm, colback=red!5,colframe=red!80!black,boxrule=0.5mm, + attach boxed title to top left={xshift=1cm,yshift*=1mm-\tcboxedtitleheight}, varwidth boxed title*=-3cm, + boxed title style={frame code={ + \path[fill=tcbcolback] + ([yshift=-1mm,xshift=-1mm]frame.north west) + arc[start angle=0,end angle=180,radius=1mm] + ([yshift=-1mm,xshift=1mm]frame.north east) + arc[start angle=180,end angle=0,radius=1mm]; + \path[left color=tcbcolback!60!black,right color=tcbcolback!60!black, + middle color=tcbcolback!80!black] + ([xshift=-2mm]frame.north west) -- ([xshift=2mm]frame.north east) + [rounded corners=1mm]-- ([xshift=1mm,yshift=-1mm]frame.north east) + -- (frame.south east) -- (frame.south west) + -- ([xshift=-1mm,yshift=-1mm]frame.north west) + [sharp corners]-- cycle; + },interior engine=empty, + }, + fonttitle=\bfseries, + title={#2},#1}{def} +\newtcbtheorem[number within=chapter]{definition}{Definition}{enhanced, + before skip=2mm,after skip=2mm, colback=red!5,colframe=red!80!black,boxrule=0.5mm, + attach boxed title to top left={xshift=1cm,yshift*=1mm-\tcboxedtitleheight}, varwidth boxed title*=-3cm, + boxed title style={frame code={ + \path[fill=tcbcolback] + ([yshift=-1mm,xshift=-1mm]frame.north west) + arc[start angle=0,end angle=180,radius=1mm] + ([yshift=-1mm,xshift=1mm]frame.north east) + arc[start angle=180,end angle=0,radius=1mm]; + \path[left color=tcbcolback!60!black,right color=tcbcolback!60!black, + middle color=tcbcolback!80!black] + ([xshift=-2mm]frame.north west) -- ([xshift=2mm]frame.north east) + [rounded corners=1mm]-- ([xshift=1mm,yshift=-1mm]frame.north east) + -- (frame.south east) -- (frame.south west) + -- ([xshift=-1mm,yshift=-1mm]frame.north west) + [sharp corners]-- cycle; + },interior engine=empty, + }, + fonttitle=\bfseries, + title={#2},#1}{def} + + + +%================================ +% Solution BOX +%================================ + +\makeatletter +\newtcbtheorem{question}{Question}{enhanced, + breakable, + colback=white, + colframe=myb!80!black, + attach boxed title to top left={yshift*=-\tcboxedtitleheight}, + fonttitle=\bfseries, + title={#2}, + boxed title size=title, + boxed title style={% + sharp corners, + rounded corners=northwest, + colback=tcbcolframe, + boxrule=0pt, + }, + underlay boxed title={% + \path[fill=tcbcolframe] (title.south west)--(title.south east) + to[out=0, in=180] ([xshift=5mm]title.east)-- + (title.center-|frame.east) + [rounded corners=\kvtcb@arc] |- + (frame.north) -| cycle; + }, + #1 +}{def} +\makeatother + +%================================ +% SOLUTION BOX +%================================ + +\makeatletter +\newtcolorbox{solution}{enhanced, + breakable, + colback=white, + colframe=myg!80!black, + attach boxed title to top left={yshift*=-\tcboxedtitleheight}, + title=Solution, + boxed title size=title, + boxed title style={% + sharp corners, + rounded corners=northwest, + colback=tcbcolframe, + boxrule=0pt, + }, + underlay boxed title={% + \path[fill=tcbcolframe] (title.south west)--(title.south east) + to[out=0, in=180] ([xshift=5mm]title.east)-- + (title.center-|frame.east) + [rounded corners=\kvtcb@arc] |- + (frame.north) -| cycle; + }, +} +\makeatother + +%================================ +% Question BOX +%================================ + +\makeatletter +\newtcbtheorem{qstion}{Question}{enhanced, + breakable, + colback=white, + colframe=mygr, + attach boxed title to top left={yshift*=-\tcboxedtitleheight}, + fonttitle=\bfseries, + title={#2}, + boxed title size=title, + boxed title style={% + sharp corners, + rounded corners=northwest, + colback=tcbcolframe, + boxrule=0pt, + }, + underlay boxed title={% + \path[fill=tcbcolframe] (title.south west)--(title.south east) + to[out=0, in=180] ([xshift=5mm]title.east)-- + (title.center-|frame.east) + [rounded corners=\kvtcb@arc] |- + (frame.north) -| cycle; + }, + #1 +}{def} +\makeatother + +\newtcbtheorem[number within=chapter]{wconc}{Wrong Concept}{ + breakable, + enhanced, + colback=white, + colframe=myr, + arc=0pt, + outer arc=0pt, + fonttitle=\bfseries\sffamily\large, + colbacktitle=myr, + attach boxed title to top left={}, + boxed title style={ + enhanced, + skin=enhancedfirst jigsaw, + arc=3pt, + bottom=0pt, + interior style={fill=myr} + }, + #1 +}{def} + + + +%================================ +% NOTE BOX +%================================ + +\usetikzlibrary{arrows,calc,shadows.blur} +\tcbuselibrary{skins} +\newtcolorbox{note}[1][]{% + enhanced jigsaw, + colback=gray!20!white,% + colframe=gray!80!black, + size=small, + boxrule=1pt, + title=\textbf{Note:}, + halign title=flush center, + coltitle=black, + breakable, + drop shadow=black!50!white, + attach boxed title to top left={xshift=1cm,yshift=-\tcboxedtitleheight/2,yshifttext=-\tcboxedtitleheight/2}, + minipage boxed title=1.5cm, + boxed title style={% + colback=white, + size=fbox, + boxrule=1pt, + boxsep=2pt, + underlay={% + \coordinate (dotA) at ($(interior.west) + (-0.5pt,0)$); + \coordinate (dotB) at ($(interior.east) + (0.5pt,0)$); + \begin{scope} + \clip (interior.north west) rectangle ([xshift=3ex]interior.east); + \filldraw [white, blur shadow={shadow opacity=60, shadow yshift=-.75ex}, rounded corners=2pt] (interior.north west) rectangle (interior.south east); + \end{scope} + \begin{scope}[gray!80!black] + \fill (dotA) circle (2pt); + \fill (dotB) circle (2pt); + \end{scope} + }, + }, + #1, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% SELF MADE COMMANDS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\newcommand{\thm}[2]{\begin{Theorem}{#1}{}#2\end{Theorem}} +\newcommand{\cor}[2]{\begin{Corollary}{#1}{}#2\end{Corollary}} +\newcommand{\rvw}[2]{\begin{Review}{#1}{}#2\end{Review}} +\newcommand{\mthd}[2]{\begin{Method}{#1}{}#2\end{Method}} +\newcommand{\clm}[3]{\begin{claim}{#1}{#2}#3\end{claim}} +\newcommand{\wc}[2]{\begin{wconc}{#1}{}\setlength{\parindent}{1cm}#2\end{wconc}} +\newcommand{\thmcon}[1]{\begin{Theoremcon}{#1}\end{Theoremcon}} +\newcommand{\ex}[2]{\begin{Example}{#1}{}#2\end{Example}} +\newcommand{\dfn}[2]{\begin{Definition}[colbacktitle=red!75!black]{#1}{}#2\end{Definition}} +\newcommand{\dfnc}[2]{\begin{definition}[colbacktitle=red!75!black]{#1}{}#2\end{definition}} +\newcommand{\qs}[2]{\begin{question}{#1}{}#2\end{question}} +\newcommand{\pf}[2]{\begin{myproof}[#1]#2\end{myproof}} +\newcommand{\nt}[1]{\begin{note}#1\end{note}} + +\newcommand*\circled[1]{\tikz[baseline=(char.base)]{ + \node[shape=circle,draw,inner sep=1pt] (char) {#1};}} +\newcommand\getcurrentref[1]{% + \ifnumequal{\value{#1}}{0} + {??} + {\the\value{#1}}% +} +\newcommand{\getCurrentSectionNumber}{\getcurrentref{section}} +\newenvironment{myproof}[1][\proofname]{% + \proof[\bfseries #1: ]% +}{\endproof} + +\newcommand{\mclm}[2]{\begin{myclaim}[#1]#2\end{myclaim}} +\newenvironment{myclaim}[1][\claimname]{\proof[\bfseries #1: ]}{} + +\newcounter{mylabelcounter} + +\makeatletter +\newcommand{\setword}[2]{% + \phantomsection + #1\def\@currentlabel{\unexpanded{#1}}\label{#2}% +} +\makeatother + + + + +\tikzset{ + symbol/.style={ + draw=none, + every to/.append style={ + edge node={node [sloped, allow upside down, auto=false]{$#1$}}} + } +} + + +% deliminators +\DeclarePairedDelimiter{\abs}{\lvert}{\rvert} +\DeclarePairedDelimiter{\norm}{\lVert}{\rVert} + +\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil} +\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor} +\DeclarePairedDelimiter{\round}{\lfloor}{\rceil} + +\newsavebox\diffdbox +\newcommand{\slantedromand}{{\mathpalette\makesl{d}}} +\newcommand{\makesl}[2]{% +\begingroup +\sbox{\diffdbox}{$\mathsurround=0pt#1\mathrm{#2}$}% +\pdfsave +\pdfsetmatrix{1 0 0.2 1}% +\rlap{\usebox{\diffdbox}}% +\pdfrestore +\hskip\wd\diffdbox +\endgroup +} +\newcommand{\dd}[1][]{\ensuremath{\mathop{}\!\ifstrempty{#1}{% +\slantedromand\@ifnextchar^{\hspace{0.2ex}}{\hspace{0.1ex}}}% +{\slantedromand\hspace{0.2ex}^{#1}}}} +\ProvideDocumentCommand\dv{o m g}{% + \ensuremath{% + \IfValueTF{#3}{% + \IfNoValueTF{#1}{% + \frac{\dd #2}{\dd #3}% + }{% + \frac{\dd^{#1} #2}{\dd #3^{#1}}% + }% + }{% + \IfNoValueTF{#1}{% + \frac{\dd}{\dd #2}% + }{% + \frac{\dd^{#1}}{\dd #2^{#1}}% + }% + }% + }% +} +\providecommand*{\pdv}[3][]{\frac{\partial^{#1}#2}{\partial#3^{#1}}} +% - others +\DeclareMathOperator{\Lap}{\mathcal{L}} +\DeclareMathOperator{\Var}{Var} % varience +\DeclareMathOperator{\Cov}{Cov} % covarience +\DeclareMathOperator{\E}{E} % expected + +% Since the amsthm package isn't loaded + +% I prefer the slanted \leq +\let\oldleq\leq % save them in case they're every wanted +\let\oldgeq\geq +\renewcommand{\leq}{\leqslant} +\renewcommand{\geq}{\geqslant} + +% % redefine matrix env to allow for alignment, use r as default +% \renewcommand*\env@matrix[1][r]{\hskip -\arraycolsep +% \let\@ifnextchar\new@ifnextchar +% \array{*\c@MaxMatrixCols #1}} + + +%\usepackage{framed} +%\usepackage{titletoc} +%\usepackage{etoolbox} +%\usepackage{lmodern} + + +%\patchcmd{\tableofcontents}{\contentsname}{\sffamily\contentsname}{}{} + +%\renewenvironment{leftbar} +%{\def\FrameCommand{\hspace{6em}% +% {\color{myyellow}\vrule width 2pt depth 6pt}\hspace{1em}}% +% \MakeFramed{\parshape 1 0cm \dimexpr\textwidth-6em\relax\FrameRestore}\vskip2pt% +%} +%{\endMakeFramed} + +%\titlecontents{chapter} +%[0em]{\vspace*{2\baselineskip}} +%{\parbox{4.5em}{% +% \hfill\Huge\sffamily\bfseries\color{myred}\thecontentspage}% +% \vspace*{-2.3\baselineskip}\leftbar\textsc{\small\chaptername~\thecontentslabel}\\\sffamily} +%{}{\endleftbar} +%\titlecontents{section} +%[8.4em] +%{\sffamily\contentslabel{3em}}{}{} +%{\hspace{0.5em}\nobreak\itshape\color{myred}\contentspage} +%\titlecontents{subsection} +%[8.4em] +%{\sffamily\contentslabel{3em}}{}{} +%{\hspace{0.5em}\nobreak\itshape\color{myred}\contentspage} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% TABLE OF CONTENTS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\usepackage{tikz} +\definecolor{doc}{RGB}{0,60,110} +\usepackage{titletoc} +\contentsmargin{0cm} +\titlecontents{chapter}[3.7pc] +{\addvspace{30pt}% + \begin{tikzpicture}[remember picture, overlay]% + \draw[fill=doc!60,draw=doc!60] (-7,-.1) rectangle (-0.9,.5);% + \pgftext[left,x=-3.5cm,y=0.2cm]{\color{white}\Large\sc\bfseries Chapter\ \thecontentslabel};% + \end{tikzpicture}\color{doc!60}\large\sc\bfseries}% +{} +{} +{\;\titlerule\;\large\sc\bfseries Page \thecontentspage + \begin{tikzpicture}[remember picture, overlay] + \draw[fill=doc!60,draw=doc!60] (2pt,0) rectangle (4,0.1pt); + \end{tikzpicture}}% +\titlecontents{section}[3.7pc] +{\addvspace{2pt}} +{\contentslabel[\thecontentslabel]{2pc}} +{} +{\hfill\small \thecontentspage} +[] +\titlecontents*{subsection}[3.7pc] +{\addvspace{-1pt}\small} +{} +{} +{\ --- \small\thecontentspage} +[ \textbullet\ ][] + +\makeatletter +\renewcommand{\tableofcontents}{% + \chapter*{% + \vspace*{-20\p@}% + \begin{tikzpicture}[remember picture, overlay]% + \pgftext[right,x=15cm,y=0.2cm]{\color{doc!60}\Huge\sc\bfseries \contentsname};% + \draw[fill=doc!60,draw=doc!60] (13,-.75) rectangle (20,1);% + \clip (13,-.75) rectangle (20,1); + \pgftext[right,x=15cm,y=0.2cm]{\color{white}\Huge\sc\bfseries \contentsname};% + \end{tikzpicture}}% + \@starttoc{toc}} +\makeatother + diff --git a/6th-Semester-Spring-2024/DSP/PracticeProblems/q1_practice.md b/6th-Semester-Spring-2024/DSP/PracticeProblems/q1_practice.md new file mode 100644 index 0000000..69162e3 --- /dev/null +++ b/6th-Semester-Spring-2024/DSP/PracticeProblems/q1_practice.md @@ -0,0 +1,21 @@ +# Quiz 1 Preparation - Aidan Sharpe +## Question 1 +Find the energy and average power of $x(n) = e^{j 2\pi n / 3}$ + +Energy of x[n]: Infinity +Power of x[n]: 1.0 +## Question 2 +Is $x(n - \pi)$ a valid discrete signal? + +No +## Question 3 +Consider the system $y[n] = S[x[n]] = e^{n+3}\cos(n-5)x[n-4]$. Is the system linear, time-invariant, causal, and BIBO stable? + +Homogeneous: True + +Superposition: True + +## Quesiton 4 +Consider the LTI sstem with impulse response $h[n] = u[n]$. If the input x[n] = n (0.3)^n u[n]$ and the output is $y[n]$, calculate: +### a) +$y(-1)$ diff --git a/6th-Semester-Spring-2024/DSP/PracticeProblems/quiz1.py b/6th-Semester-Spring-2024/DSP/PracticeProblems/quiz1.py new file mode 100644 index 0000000..88d0329 --- /dev/null +++ b/6th-Semester-Spring-2024/DSP/PracticeProblems/quiz1.py @@ -0,0 +1,64 @@ +import numpy as np +import matplotlib.pyplot as plt + +PI = np.pi +INF = 10 + +print("# Quiz 1 Preparation - Aidan Sharpe") + +print("""## Question 1 +Find the energy and average power of $x(n) = e^{j 2\pi n / 3}$ +""") + +def x_1(n): + return np.exp(2j*PI*n/3) + +x_n = x_1(np.arange(-INF, INF)) +E_x = np.sum( np.abs(x_n)**2 ) +print("Energy of x[n]:", E_x if E_x < INF else "Infinity") + +N = 3 +x_n = x_1(np.arange(0, N)) +P_x = (1/N) * np.sum( np.abs(x_n)**2 ) +print("Power of x[n]:", P_x if P_x < INF else "Infinity") + +print("""## Question 2 +Is $x(n - \pi)$ a valid discrete signal? + +No""") + +print("""## Question 3 +Consider the system $y[n] = S[x[n]] = e^{n+3}\cos(n-5)x[n-4]$. Is the system linear, time-invariant, causal, and BIBO stable? +""") + +a_3 = 5 + +def S_3(x,n,a=1): + return np.exp(n+3) * np.cos(n-5) * x(n-4) * a + +def x_3_1(n): + return n*(n-1)*np.heaviside(n,0) + +def x_3_2(n): + return 5*n*np.heaviside(n,0) + +def x_3_1_2(n): + return x_3_1(n) + x_3_2(n) + +S_ax_3 = S_3(x_3_1, np.arange(-INF, INF), a=a_3) +y_3 = S_3(x_3_1, np.arange(-INF, INF)) +print("Homogeneous:", abs(sum(S_ax_3 - a_3*y_3)) < 0.01, '\n') +S_x1_x2_3 = S_3(x_3_1_2, np.arange(-INF, INF)) +y1_3 = S_3(x_3_1, np.arange(-INF,INF)) +y2_3 = S_3(x_3_2, np.arange(-INF, INF)) + +print("Superposition:", abs(sum(S_x1_x2_3 - (y1_3 + y2_3))) < 0.01, '\n') + + + +print("""## Quesiton 4 +Consider the LTI sstem with impulse response $h[n] = u[n]$. If the input x[n] = n (0.3)^n u[n]$ and the output is $y[n]$, calculate: +### a) +$y(-1)$""") + + diff --git a/6th-Semester-Spring-2024/DSP/Quizzes/answer_sheet_1.docx b/6th-Semester-Spring-2024/DSP/Quizzes/answer_sheet_1.docx new file mode 100644 index 0000000..dfb58cc Binary files /dev/null and b/6th-Semester-Spring-2024/DSP/Quizzes/answer_sheet_1.docx differ diff --git a/6th-Semester-Spring-2024/DSP/Quizzes/quiz1.pdf b/6th-Semester-Spring-2024/DSP/Quizzes/quiz1.pdf new file mode 100644 index 0000000..fd192aa Binary files /dev/null and b/6th-Semester-Spring-2024/DSP/Quizzes/quiz1.pdf differ diff --git a/6th-Semester-Spring-2024/EnI/Assignments/EngagementHours/Engagement Hours Summary Template.docx b/6th-Semester-Spring-2024/EnI/Assignments/EngagementHours/Engagement Hours Summary Template.docx new file mode 100644 index 0000000..3ecb8f7 Binary files /dev/null and b/6th-Semester-Spring-2024/EnI/Assignments/EngagementHours/Engagement Hours Summary Template.docx differ diff --git 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stream + 0 named destinations out of 1000 (max. 500000) + 1 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/6th-Semester-Spring-2024/EnI/Assignments/EngagementHours/EngagementHoursTemplate.pdf b/6th-Semester-Spring-2024/EnI/Assignments/EngagementHours/EngagementHoursTemplate.pdf new file mode 100644 index 0000000..f47ad39 Binary files /dev/null and b/6th-Semester-Spring-2024/EnI/Assignments/EngagementHours/EngagementHoursTemplate.pdf differ diff --git a/6th-Semester-Spring-2024/EnI/Assignments/EngagementHours/EngagementHoursTemplate.synctex.gz b/6th-Semester-Spring-2024/EnI/Assignments/EngagementHours/EngagementHoursTemplate.synctex.gz new file mode 100644 index 0000000..749f16f Binary files /dev/null and b/6th-Semester-Spring-2024/EnI/Assignments/EngagementHours/EngagementHoursTemplate.synctex.gz differ diff --git a/6th-Semester-Spring-2024/EnI/Assignments/EngagementHours/EngagementHoursTemplate.tex b/6th-Semester-Spring-2024/EnI/Assignments/EngagementHours/EngagementHoursTemplate.tex new file mode 100644 index 0000000..8b2b803 --- /dev/null +++ b/6th-Semester-Spring-2024/EnI/Assignments/EngagementHours/EngagementHoursTemplate.tex @@ -0,0 +1,27 @@ +\documentclass{article} +\usepackage{lscape} + +\begin{document} +\begin{landscape} +Aidan Sharpe + +Honors Entrepreneurship \& Innovation -- ENT 06240 Section 7 + +Entrepreneurial Engagement Hours Assignment + +Professor Payton + +\date{} + +\textbf{Summary of Engagement Hours (Total of Eight Hours Required)} + +\begin{center} + \begin{tabular}[]{ p{3cm} | p{3cm} | p{3cm} | p{3cm} | p{3cm}} + \textbf{Event Title} & \textbf{Event Date \& Time} & \textbf{\# Hours Planned/ Completed} & \textbf{Brief Description} & \textbf{Rationale for Selection} \\ + \hline + Lunch and Learn & Wednsesday, February 14\textsuperscript{th}, 11:15---13:15 & 1hr & Join the Rowan Center for Innovation \& Entrepreneurship for Lunch and Learn where you’ll receive tangible tools on how to accelerate your ideas, startup or take a step further in learning how to become a successful business leader by playing 'Unnecessary Inventions". & It's basically the first event to fit in my schedule. +\end{tabular} +\end{center} + +\end{landscape} +\end{document} diff --git a/6th-Semester-Spring-2024/EnI/Assignments/LinkedIn-Summary/LinkedIn-Summary.aux b/6th-Semester-Spring-2024/EnI/Assignments/LinkedIn-Summary/LinkedIn-Summary.aux new file mode 100644 index 0000000..bd68a1c --- /dev/null +++ b/6th-Semester-Spring-2024/EnI/Assignments/LinkedIn-Summary/LinkedIn-Summary.aux @@ -0,0 +1,21 @@ +\relax +\providecommand\babel@aux[2]{} +\@nameuse{bbl@beforestart} +\abx@aux@refcontext{nty/global//global/global} +\providecommand\hyper@newdestlabel[2]{} +\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} +\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined +\global\let\oldnewlabel\newlabel +\gdef\newlabel#1#2{\newlabelxx{#1}#2} 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type="singlevalued"> + <bcf:key>uniquebaretitle</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>uniquework</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useprefix</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useafterword</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useannotator</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useauthor</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>usebookauthor</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>usecommentator</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useeditor</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useeditora</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useeditorb</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useeditorc</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useforeword</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useholder</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useintroduction</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>usenamea</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>usenameb</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>usenamec</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>usetranslator</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useshortauthor</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useshorteditor</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + </bcf:options> + <!-- inreference --> + <bcf:options component="biblatex" type="inreference"> + <bcf:option type="singlevalued"> + <bcf:key>labelalpha</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="multivalued"> + <bcf:key>labelnamespec</bcf:key> + <bcf:value order="1">shortauthor</bcf:value> + <bcf:value order="2">author</bcf:value> + <bcf:value order="3">shorteditor</bcf:value> + <bcf:value order="4">editor</bcf:value> + <bcf:value order="5">translator</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>labeltitle</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="multivalued"> + <bcf:key>labeltitlespec</bcf:key> + <bcf:value order="1">shorttitle</bcf:value> + <bcf:value order="2">title</bcf:value> + <bcf:value order="3">maintitle</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>labeltitleyear</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>labeldateparts</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="multivalued"> + <bcf:key>labeldatespec</bcf:key> + <bcf:value order="1" type="field">date</bcf:value> + <bcf:value order="2" type="field">year</bcf:value> + <bcf:value order="3" type="field">eventdate</bcf:value> + <bcf:value order="4" type="field">origdate</bcf:value> + <bcf:value order="5" type="field">urldate</bcf:value> + <bcf:value order="6" type="string">nodate</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>maxalphanames</bcf:key> + <bcf:value>3</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>maxbibnames</bcf:key> + <bcf:value>2</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>maxcitenames</bcf:key> + <bcf:value>2</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>maxsortnames</bcf:key> + <bcf:value>2</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>maxitems</bcf:key> + <bcf:value>3</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>minalphanames</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>minbibnames</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>mincitenames</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>minsortnames</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>minitems</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>nohashothers</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>noroman</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>nosortothers</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>singletitle</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>skipbib</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>skipbiblist</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>skiplab</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>uniquelist</bcf:key> + <bcf:value>false</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>uniquename</bcf:key> + <bcf:value>init</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>uniqueprimaryauthor</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>uniquetitle</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>uniquebaretitle</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>uniquework</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useprefix</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useafterword</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useannotator</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useauthor</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>usebookauthor</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>usecommentator</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useeditor</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useeditora</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useeditorb</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useeditorc</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useforeword</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useholder</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useintroduction</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>usenamea</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>usenameb</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>usenamec</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>usetranslator</bcf:key> + <bcf:value>0</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useshortauthor</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + <bcf:option type="singlevalued"> + <bcf:key>useshorteditor</bcf:key> + <bcf:value>1</bcf:value> + </bcf:option> + </bcf:options> + <!-- BIBLATEX OPTION SCOPE --> + <bcf:optionscope type="GLOBAL"> + <bcf:option datatype="xml">datamodel</bcf:option> + <bcf:option datatype="xml">labelalphanametemplate</bcf:option> + <bcf:option datatype="xml">labelalphatemplate</bcf:option> + <bcf:option datatype="xml">inheritance</bcf:option> + <bcf:option datatype="xml">translit</bcf:option> + <bcf:option datatype="xml">uniquenametemplate</bcf:option> + <bcf:option datatype="xml">sortingnamekeytemplate</bcf:option> + <bcf:option datatype="xml">sortingtemplate</bcf:option> + <bcf:option datatype="xml">extradatespec</bcf:option> + <bcf:option datatype="xml">labelnamespec</bcf:option> + <bcf:option datatype="xml">labeltitlespec</bcf:option> + <bcf:option datatype="xml">labeldatespec</bcf:option> + <bcf:option datatype="string">controlversion</bcf:option> + <bcf:option datatype="string">alphaothers</bcf:option> + <bcf:option datatype="string">sortalphaothers</bcf:option> + <bcf:option datatype="string">presort</bcf:option> + <bcf:option datatype="string">texencoding</bcf:option> + <bcf:option datatype="string">bibencoding</bcf:option> + <bcf:option datatype="string">sortingtemplatename</bcf:option> + <bcf:option datatype="string">sortlocale</bcf:option> + <bcf:option datatype="string">language</bcf:option> + <bcf:option datatype="string">autolang</bcf:option> + <bcf:option datatype="string">langhook</bcf:option> + <bcf:option datatype="string">indexing</bcf:option> + <bcf:option datatype="string">hyperref</bcf:option> + <bcf:option datatype="string">backrefsetstyle</bcf:option> + <bcf:option datatype="string">block</bcf:option> + <bcf:option datatype="string">pagetracker</bcf:option> + <bcf:option datatype="string">citecounter</bcf:option> + <bcf:option datatype="string">citetracker</bcf:option> + <bcf:option datatype="string">ibidtracker</bcf:option> + <bcf:option datatype="string">idemtracker</bcf:option> + <bcf:option datatype="string">opcittracker</bcf:option> + <bcf:option datatype="string">loccittracker</bcf:option> + <bcf:option datatype="string">labeldate</bcf:option> + <bcf:option datatype="string">labeltime</bcf:option> + <bcf:option datatype="string">dateera</bcf:option> + <bcf:option datatype="string">date</bcf:option> + <bcf:option datatype="string">time</bcf:option> + <bcf:option datatype="string">eventdate</bcf:option> + <bcf:option datatype="string">eventtime</bcf:option> + <bcf:option datatype="string">origdate</bcf:option> + <bcf:option datatype="string">origtime</bcf:option> + <bcf:option datatype="string">urldate</bcf:option> + <bcf:option datatype="string">urltime</bcf:option> + <bcf:option datatype="string">alldatesusetime</bcf:option> + <bcf:option datatype="string">alldates</bcf:option> + <bcf:option datatype="string">alltimes</bcf:option> + <bcf:option datatype="string">gregorianstart</bcf:option> + <bcf:option datatype="string">autocite</bcf:option> + <bcf:option datatype="string">notetype</bcf:option> + <bcf:option datatype="string">uniquelist</bcf:option> + <bcf:option datatype="string">uniquename</bcf:option> + <bcf:option datatype="string">refsection</bcf:option> + <bcf:option datatype="string">refsegment</bcf:option> + <bcf:option datatype="string">citereset</bcf:option> + <bcf:option datatype="string">sortlos</bcf:option> + <bcf:option datatype="string">babel</bcf:option> + <bcf:option datatype="string">datelabel</bcf:option> + <bcf:option datatype="string">backrefstyle</bcf:option> + <bcf:option datatype="string">arxiv</bcf:option> + <bcf:option datatype="string">containerized</bcf:option> + <bcf:option datatype="string">nametracker</bcf:option> + <bcf:option datatype="boolean">familyinits</bcf:option> + <bcf:option datatype="boolean">giveninits</bcf:option> + <bcf:option datatype="boolean">prefixinits</bcf:option> + <bcf:option datatype="boolean">suffixinits</bcf:option> + <bcf:option datatype="boolean">useafterword</bcf:option> + <bcf:option datatype="boolean">useannotator</bcf:option> + <bcf:option datatype="boolean">useauthor</bcf:option> + <bcf:option datatype="boolean">usebookauthor</bcf:option> + <bcf:option datatype="boolean">usecommentator</bcf:option> + <bcf:option datatype="boolean">useeditor</bcf:option> + <bcf:option datatype="boolean">useeditora</bcf:option> + <bcf:option datatype="boolean">useeditorb</bcf:option> + <bcf:option datatype="boolean">useeditorc</bcf:option> + <bcf:option datatype="boolean">useforeword</bcf:option> + <bcf:option datatype="boolean">useholder</bcf:option> + <bcf:option datatype="boolean">useintroduction</bcf:option> + <bcf:option datatype="boolean">usenamea</bcf:option> + <bcf:option datatype="boolean">usenameb</bcf:option> + <bcf:option datatype="boolean">usenamec</bcf:option> + <bcf:option datatype="boolean">usetranslator</bcf:option> + <bcf:option datatype="boolean">useshortauthor</bcf:option> + <bcf:option datatype="boolean">useshorteditor</bcf:option> + <bcf:option datatype="boolean">debug</bcf:option> + <bcf:option datatype="boolean">loadfiles</bcf:option> + <bcf:option datatype="boolean">safeinputenc</bcf:option> + <bcf:option datatype="boolean">sortcase</bcf:option> + <bcf:option datatype="boolean">sortupper</bcf:option> + <bcf:option datatype="boolean">terseinits</bcf:option> + <bcf:option datatype="boolean">abbreviate</bcf:option> + <bcf:option datatype="boolean">dateabbrev</bcf:option> + <bcf:option datatype="boolean">clearlang</bcf:option> + <bcf:option datatype="boolean">sortcites</bcf:option> + <bcf:option datatype="boolean">sortsets</bcf:option> + <bcf:option datatype="boolean">backref</bcf:option> + <bcf:option datatype="boolean">backreffloats</bcf:option> + <bcf:option datatype="boolean">trackfloats</bcf:option> + <bcf:option datatype="boolean">parentracker</bcf:option> + <bcf:option datatype="boolean">labeldateusetime</bcf:option> + <bcf:option datatype="boolean">datecirca</bcf:option> + <bcf:option datatype="boolean">dateuncertain</bcf:option> + <bcf:option datatype="boolean">dateusetime</bcf:option> + <bcf:option datatype="boolean">eventdateusetime</bcf:option> + <bcf:option datatype="boolean">origdateusetime</bcf:option> + <bcf:option datatype="boolean">urldateusetime</bcf:option> + <bcf:option datatype="boolean">julian</bcf:option> + <bcf:option datatype="boolean">datezeros</bcf:option> + <bcf:option datatype="boolean">timezeros</bcf:option> + <bcf:option datatype="boolean">timezones</bcf:option> + <bcf:option datatype="boolean">seconds</bcf:option> + <bcf:option datatype="boolean">autopunct</bcf:option> + <bcf:option datatype="boolean">punctfont</bcf:option> + <bcf:option datatype="boolean">labelnumber</bcf:option> + <bcf:option datatype="boolean">labelalpha</bcf:option> + <bcf:option datatype="boolean">labeltitle</bcf:option> + <bcf:option datatype="boolean">labeltitleyear</bcf:option> + <bcf:option datatype="boolean">labeldateparts</bcf:option> + <bcf:option datatype="boolean">pluralothers</bcf:option> + <bcf:option datatype="boolean">nohashothers</bcf:option> + <bcf:option datatype="boolean">nosortothers</bcf:option> + <bcf:option datatype="boolean">noroman</bcf:option> + <bcf:option datatype="boolean">singletitle</bcf:option> + <bcf:option datatype="boolean">uniquetitle</bcf:option> + <bcf:option datatype="boolean">uniquebaretitle</bcf:option> + <bcf:option datatype="boolean">uniquework</bcf:option> + <bcf:option datatype="boolean">uniqueprimaryauthor</bcf:option> + <bcf:option datatype="boolean">defernumbers</bcf:option> + <bcf:option datatype="boolean">locallabelwidth</bcf:option> + <bcf:option datatype="boolean">bibwarn</bcf:option> + <bcf:option datatype="boolean">useprefix</bcf:option> + <bcf:option datatype="boolean">skipbib</bcf:option> + <bcf:option datatype="boolean">skipbiblist</bcf:option> + <bcf:option datatype="boolean">skiplab</bcf:option> + <bcf:option datatype="boolean">dataonly</bcf:option> + <bcf:option datatype="boolean">defernums</bcf:option> + <bcf:option datatype="boolean">firstinits</bcf:option> + <bcf:option datatype="boolean">sortfirstinits</bcf:option> + <bcf:option datatype="boolean">sortgiveninits</bcf:option> + <bcf:option datatype="boolean">labelyear</bcf:option> + <bcf:option datatype="boolean">isbn</bcf:option> + <bcf:option datatype="boolean">url</bcf:option> + <bcf:option datatype="boolean">doi</bcf:option> + <bcf:option datatype="boolean">eprint</bcf:option> + <bcf:option datatype="boolean">related</bcf:option> + <bcf:option datatype="boolean">dashed</bcf:option> + <bcf:option datatype="boolean">annotation</bcf:option> + <bcf:option datatype="boolean">showlocation</bcf:option> + <bcf:option datatype="boolean">longdash</bcf:option> + <bcf:option datatype="boolean">noremoteinfo</bcf:option> + <bcf:option datatype="boolean">isan</bcf:option> + <bcf:option datatype="boolean">ismn</bcf:option> + <bcf:option datatype="boolean">isrn</bcf:option> + <bcf:option datatype="boolean">issn</bcf:option> + <bcf:option datatype="boolean">firstlonghand</bcf:option> + <bcf:option datatype="boolean">nofullfootnote</bcf:option> + <bcf:option datatype="boolean">mancitepar</bcf:option> + <bcf:option datatype="boolean">footnoterulestrict</bcf:option> + <bcf:option datatype="boolean">mladraft</bcf:option> + <bcf:option datatype="boolean">bibtexcaseprotection</bcf:option> + <bcf:option datatype="integer">mincrossrefs</bcf:option> + <bcf:option datatype="integer">minxrefs</bcf:option> + <bcf:option datatype="integer">maxnames</bcf:option> + <bcf:option datatype="integer">minnames</bcf:option> + <bcf:option datatype="integer">maxbibnames</bcf:option> + <bcf:option datatype="integer">minbibnames</bcf:option> + <bcf:option datatype="integer">maxcitenames</bcf:option> + <bcf:option datatype="integer">mincitenames</bcf:option> + <bcf:option datatype="integer">maxsortnames</bcf:option> + <bcf:option datatype="integer">minsortnames</bcf:option> + <bcf:option datatype="integer">maxitems</bcf:option> + <bcf:option datatype="integer">minitems</bcf:option> + <bcf:option datatype="integer">maxalphanames</bcf:option> + <bcf:option datatype="integer">minalphanames</bcf:option> + <bcf:option datatype="integer">maxparens</bcf:option> + <bcf:option datatype="integer">dateeraauto</bcf:option> + </bcf:optionscope> + <bcf:optionscope type="ENTRYTYPE"> + <bcf:option datatype="string">alphaothers</bcf:option> + <bcf:option datatype="string">sortalphaothers</bcf:option> + <bcf:option datatype="string">presort</bcf:option> + <bcf:option datatype="string">indexing</bcf:option> + <bcf:option datatype="string">citetracker</bcf:option> + <bcf:option datatype="string">ibidtracker</bcf:option> + <bcf:option datatype="string">idemtracker</bcf:option> + <bcf:option datatype="string">opcittracker</bcf:option> + <bcf:option datatype="string">loccittracker</bcf:option> + <bcf:option datatype="string">uniquelist</bcf:option> + <bcf:option datatype="string">uniquename</bcf:option> + <bcf:option datatype="boolean">familyinits</bcf:option> + <bcf:option datatype="boolean">giveninits</bcf:option> + <bcf:option datatype="boolean">prefixinits</bcf:option> + <bcf:option datatype="boolean">suffixinits</bcf:option> + <bcf:option datatype="boolean">useafterword</bcf:option> + <bcf:option datatype="boolean">useannotator</bcf:option> + <bcf:option datatype="boolean">useauthor</bcf:option> + <bcf:option datatype="boolean">usebookauthor</bcf:option> + <bcf:option datatype="boolean">usecommentator</bcf:option> + <bcf:option datatype="boolean">useeditor</bcf:option> + <bcf:option datatype="boolean">useeditora</bcf:option> + <bcf:option datatype="boolean">useeditorb</bcf:option> + <bcf:option datatype="boolean">useeditorc</bcf:option> + <bcf:option datatype="boolean">useforeword</bcf:option> + <bcf:option datatype="boolean">useholder</bcf:option> + <bcf:option datatype="boolean">useintroduction</bcf:option> + <bcf:option datatype="boolean">usenamea</bcf:option> + <bcf:option datatype="boolean">usenameb</bcf:option> + <bcf:option datatype="boolean">usenamec</bcf:option> + <bcf:option datatype="boolean">usetranslator</bcf:option> + <bcf:option datatype="boolean">useshortauthor</bcf:option> + <bcf:option datatype="boolean">useshorteditor</bcf:option> + <bcf:option datatype="boolean">terseinits</bcf:option> + <bcf:option datatype="boolean">abbreviate</bcf:option> + <bcf:option datatype="boolean">dateabbrev</bcf:option> + <bcf:option datatype="boolean">clearlang</bcf:option> + <bcf:option datatype="boolean">labelnumber</bcf:option> + <bcf:option datatype="boolean">labelalpha</bcf:option> + <bcf:option datatype="boolean">labeltitle</bcf:option> + <bcf:option datatype="boolean">labeltitleyear</bcf:option> + <bcf:option datatype="boolean">labeldateparts</bcf:option> + <bcf:option datatype="boolean">nohashothers</bcf:option> + <bcf:option datatype="boolean">nosortothers</bcf:option> + <bcf:option datatype="boolean">noroman</bcf:option> + <bcf:option datatype="boolean">singletitle</bcf:option> + <bcf:option datatype="boolean">uniquetitle</bcf:option> + <bcf:option datatype="boolean">uniquebaretitle</bcf:option> + <bcf:option datatype="boolean">uniquework</bcf:option> + <bcf:option datatype="boolean">uniqueprimaryauthor</bcf:option> + <bcf:option datatype="boolean">useprefix</bcf:option> + <bcf:option datatype="boolean">skipbib</bcf:option> + <bcf:option datatype="boolean">skipbiblist</bcf:option> + <bcf:option datatype="boolean">skiplab</bcf:option> + <bcf:option datatype="boolean">dataonly</bcf:option> + <bcf:option datatype="boolean">skiplos</bcf:option> + <bcf:option datatype="boolean">labelyear</bcf:option> + <bcf:option datatype="boolean">isbn</bcf:option> + <bcf:option datatype="boolean">url</bcf:option> + <bcf:option datatype="boolean">doi</bcf:option> + <bcf:option datatype="boolean">eprint</bcf:option> + <bcf:option datatype="boolean">related</bcf:option> + <bcf:option datatype="boolean">bibtexcaseprotection</bcf:option> + <bcf:option datatype="xml">labelalphatemplate</bcf:option> + <bcf:option datatype="xml">translit</bcf:option> + <bcf:option datatype="xml">sortexclusion</bcf:option> + <bcf:option datatype="xml">sortinclusion</bcf:option> + <bcf:option datatype="xml">labelnamespec</bcf:option> + <bcf:option datatype="xml">labeltitlespec</bcf:option> + <bcf:option datatype="xml">labeldatespec</bcf:option> + <bcf:option datatype="integer">maxnames</bcf:option> + <bcf:option datatype="integer">minnames</bcf:option> + <bcf:option datatype="integer">maxbibnames</bcf:option> + <bcf:option datatype="integer">minbibnames</bcf:option> + <bcf:option datatype="integer">maxcitenames</bcf:option> + <bcf:option datatype="integer">mincitenames</bcf:option> + <bcf:option datatype="integer">maxsortnames</bcf:option> + <bcf:option datatype="integer">minsortnames</bcf:option> + <bcf:option datatype="integer">maxitems</bcf:option> + <bcf:option datatype="integer">minitems</bcf:option> + <bcf:option datatype="integer">maxalphanames</bcf:option> + <bcf:option datatype="integer">minalphanames</bcf:option> + </bcf:optionscope> + <bcf:optionscope type="ENTRY"> + <bcf:option datatype="string">noinherit</bcf:option> + <bcf:option datatype="string" backendin="sortingnamekeytemplatename,uniquenametemplatename,labelalphanametemplatename">nametemplates</bcf:option> + <bcf:option datatype="string" backendout="1">labelalphanametemplatename</bcf:option> + <bcf:option datatype="string" backendout="1">uniquenametemplatename</bcf:option> + <bcf:option datatype="string" backendout="1">sortingnamekeytemplatename</bcf:option> + <bcf:option datatype="string">presort</bcf:option> + <bcf:option datatype="string" backendout="1">indexing</bcf:option> + <bcf:option datatype="string" backendout="1">citetracker</bcf:option> + <bcf:option datatype="string" backendout="1">ibidtracker</bcf:option> + <bcf:option datatype="string" backendout="1">idemtracker</bcf:option> + <bcf:option datatype="string" backendout="1">opcittracker</bcf:option> + <bcf:option datatype="string" backendout="1">loccittracker</bcf:option> + <bcf:option datatype="string">uniquelist</bcf:option> + <bcf:option datatype="string">uniquename</bcf:option> + <bcf:option datatype="string" backendout="1">containerized</bcf:option> + <bcf:option datatype="boolean" backendout="1">familyinits</bcf:option> + <bcf:option datatype="boolean" backendout="1">giveninits</bcf:option> + <bcf:option datatype="boolean" backendout="1">prefixinits</bcf:option> + <bcf:option datatype="boolean" backendout="1">suffixinits</bcf:option> + <bcf:option datatype="boolean" backendout="1">useafterword</bcf:option> + <bcf:option datatype="boolean" backendout="1">useannotator</bcf:option> + <bcf:option datatype="boolean" backendout="1">useauthor</bcf:option> + <bcf:option datatype="boolean" backendout="1">usebookauthor</bcf:option> + <bcf:option datatype="boolean" backendout="1">usecommentator</bcf:option> + <bcf:option datatype="boolean" backendout="1">useeditor</bcf:option> + <bcf:option datatype="boolean" backendout="1">useeditora</bcf:option> + <bcf:option datatype="boolean" backendout="1">useeditorb</bcf:option> + <bcf:option datatype="boolean" backendout="1">useeditorc</bcf:option> + <bcf:option datatype="boolean" backendout="1">useforeword</bcf:option> + <bcf:option datatype="boolean" backendout="1">useholder</bcf:option> + <bcf:option datatype="boolean" backendout="1">useintroduction</bcf:option> + <bcf:option datatype="boolean" backendout="1">usenamea</bcf:option> + <bcf:option datatype="boolean" backendout="1">usenameb</bcf:option> + <bcf:option datatype="boolean" backendout="1">usenamec</bcf:option> + <bcf:option datatype="boolean" backendout="1">usetranslator</bcf:option> + <bcf:option datatype="boolean" backendout="1">useshortauthor</bcf:option> + <bcf:option datatype="boolean" backendout="1">useshorteditor</bcf:option> + <bcf:option datatype="boolean" backendout="1">terseinits</bcf:option> + <bcf:option datatype="boolean" backendout="1">abbreviate</bcf:option> + <bcf:option datatype="boolean" backendout="1">dateabbrev</bcf:option> + <bcf:option datatype="boolean" backendout="1">clearlang</bcf:option> + <bcf:option datatype="boolean" backendout="1">labelnumber</bcf:option> + <bcf:option datatype="boolean" backendout="1">labelalpha</bcf:option> + <bcf:option datatype="boolean" backendout="1">labeltitle</bcf:option> + <bcf:option datatype="boolean" backendout="1">labeltitleyear</bcf:option> + <bcf:option datatype="boolean" backendout="1">labeldateparts</bcf:option> + <bcf:option datatype="boolean">nohashothers</bcf:option> + <bcf:option datatype="boolean">nosortothers</bcf:option> + <bcf:option datatype="boolean">noroman</bcf:option> + <bcf:option datatype="boolean">singletitle</bcf:option> + <bcf:option datatype="boolean">uniquetitle</bcf:option> + <bcf:option datatype="boolean">uniquebaretitle</bcf:option> + <bcf:option datatype="boolean">uniquework</bcf:option> + <bcf:option datatype="boolean">uniqueprimaryauthor</bcf:option> + <bcf:option datatype="boolean" backendout="1">useprefix</bcf:option> + <bcf:option datatype="boolean" backendout="1">skipbib</bcf:option> + <bcf:option datatype="boolean" backendout="1">skipbiblist</bcf:option> + <bcf:option datatype="boolean" backendout="1">skiplab</bcf:option> + <bcf:option datatype="boolean" backendin="uniquename=false,uniquelist=false,skipbib=true,skipbiblist=true,skiplab=true">dataonly</bcf:option> + <bcf:option datatype="boolean" backendout="1">skiplos</bcf:option> + <bcf:option datatype="boolean" backendout="1">isbn</bcf:option> + <bcf:option datatype="boolean" backendout="1">url</bcf:option> + <bcf:option datatype="boolean" backendout="1">doi</bcf:option> + <bcf:option datatype="boolean" backendout="1">eprint</bcf:option> + <bcf:option datatype="boolean" backendout="1">related</bcf:option> + <bcf:option datatype="boolean" backendout="1">totalnames</bcf:option> + <bcf:option datatype="boolean" backendout="1">uniquetranslator</bcf:option> + <bcf:option datatype="boolean" backendout="1">uniquenamea</bcf:option> + <bcf:option datatype="boolean" backendout="1">uniquenameb</bcf:option> + <bcf:option datatype="boolean" backendout="1">uniquenamec</bcf:option> + <bcf:option datatype="boolean" backendout="1">showlocation</bcf:option> + <bcf:option datatype="boolean" backendout="1">datebrackets</bcf:option> + <bcf:option datatype="boolean" backendout="1">noremoteinfo</bcf:option> + <bcf:option datatype="boolean" backendout="1">nodate</bcf:option> + <bcf:option datatype="boolean" backendout="1">bibtexcaseprotection</bcf:option> + <bcf:option datatype="integer" backendin="maxcitenames,maxbibnames,maxsortnames">maxnames</bcf:option> + <bcf:option datatype="integer" backendin="mincitenames,minbibnames,minsortnames">minnames</bcf:option> + <bcf:option datatype="integer" backendout="1">maxbibnames</bcf:option> + <bcf:option datatype="integer" backendout="1">minbibnames</bcf:option> + <bcf:option datatype="integer" backendout="1">maxcitenames</bcf:option> + <bcf:option datatype="integer" backendout="1">mincitenames</bcf:option> + <bcf:option datatype="integer" backendout="1">maxsortnames</bcf:option> + <bcf:option datatype="integer" backendout="1">minsortnames</bcf:option> + <bcf:option datatype="integer" backendout="1">maxitems</bcf:option> + <bcf:option datatype="integer" backendout="1">minitems</bcf:option> + <bcf:option datatype="integer" backendout="1">maxalphanames</bcf:option> + <bcf:option datatype="integer" backendout="1">minalphanames</bcf:option> + </bcf:optionscope> + <bcf:optionscope type="NAMELIST"> + <bcf:option datatype="string" backendin="sortingnamekeytemplatename,uniquenametemplatename,labelalphanametemplatename">nametemplates</bcf:option> + <bcf:option datatype="string" backendout="1">labelalphanametemplatename</bcf:option> + <bcf:option datatype="string" backendout="1">uniquenametemplatename</bcf:option> + <bcf:option datatype="string" backendout="1">sortingnamekeytemplatename</bcf:option> + <bcf:option datatype="string">uniquelist</bcf:option> + <bcf:option datatype="string">uniquename</bcf:option> + <bcf:option datatype="boolean" backendout="1">familyinits</bcf:option> + <bcf:option datatype="boolean" backendout="1">giveninits</bcf:option> + <bcf:option datatype="boolean" backendout="1">prefixinits</bcf:option> + <bcf:option datatype="boolean" backendout="1">suffixinits</bcf:option> + <bcf:option datatype="boolean" backendout="1">terseinits</bcf:option> + <bcf:option datatype="boolean">nohashothers</bcf:option> + <bcf:option datatype="boolean">nosortothers</bcf:option> + <bcf:option datatype="boolean" backendout="1">useprefix</bcf:option> + </bcf:optionscope> + <bcf:optionscope type="NAME"> + <bcf:option datatype="string" backendin="sortingnamekeytemplatename,uniquenametemplatename,labelalphanametemplatename">nametemplates</bcf:option> + <bcf:option datatype="string" backendout="1">labelalphanametemplatename</bcf:option> + <bcf:option datatype="string" backendout="1">uniquenametemplatename</bcf:option> + <bcf:option datatype="string" backendout="1">sortingnamekeytemplatename</bcf:option> + <bcf:option datatype="string">uniquename</bcf:option> + <bcf:option datatype="boolean" backendout="1">familyinits</bcf:option> + <bcf:option datatype="boolean" backendout="1">giveninits</bcf:option> + <bcf:option datatype="boolean" backendout="1">prefixinits</bcf:option> + <bcf:option datatype="boolean" backendout="1">suffixinits</bcf:option> + <bcf:option datatype="boolean" backendout="1">terseinits</bcf:option> + <bcf:option datatype="boolean" backendout="1">useprefix</bcf:option> + </bcf:optionscope> + <!-- DATAFIELDSETS --> + <bcf:datafieldset name="setnames"> + <bcf:member datatype="name" fieldtype="list"/> + </bcf:datafieldset> + <bcf:datafieldset name="settitles"> + <bcf:member field="title"/> + <bcf:member field="booktitle"/> + <bcf:member field="eventtitle"/> + <bcf:member field="issuetitle"/> + <bcf:member field="journaltitle"/> + <bcf:member field="maintitle"/> + <bcf:member field="origtitle"/> + </bcf:datafieldset> + <!-- SOURCEMAP --> + <bcf:sourcemap> + <bcf:maps datatype="bibtex" level="style"> + <bcf:map map_overwrite="1"> + <bcf:map_step map_field_source="year" map_match="[a-zA-Z]" map_final="1"/> + <bcf:map_step map_field_source="year" map_match="(.+)" map_final="1"/> + <bcf:map_step map_field_set="addendum" map_field_value="$1"/> + <bcf:map_step map_field_set="year" map_null="1"/> + </bcf:map> + <bcf:map> + <bcf:per_type>unpublished</bcf:per_type> + <bcf:map_step map_notfield="title" map_final="1"/> + <bcf:map_step map_field_source="booktitle" map_match="(.+)" map_final="1"/> + <bcf:map_step map_field_set="title" map_field_value="$1" map_final="1"/> + <bcf:map_step map_field_set="booktitle" map_null="1"/> + <bcf:map_step map_field_set="entrysubtype" map_field_value="book"/> + </bcf:map> + <bcf:map> + <bcf:per_type>video</bcf:per_type> + <bcf:map_step map_field_source="addendum" map_notmatch="mkbibemph" map_final="1"/> + <bcf:map_step map_field_source="addendum" map_match="(.+)\s+app$" map_replace="\AddToHookNext {para/begin}{\box_gclear:N \g_para_indent_box }\@centercr mkbibemph\{$1\} app"/> + </bcf:map> + <bcf:map> + <bcf:per_type>movie</bcf:per_type> + <bcf:map_step map_field_source="addendum" map_notmatch="mkbibemph" map_final="1"/> + <bcf:map_step map_field_source="addendum" map_match="(.+)\s+app$" map_replace="\AddToHookNext {para/begin}{\box_gclear:N \g_para_indent_box }\@centercr mkbibemph\{$1\} app"/> + </bcf:map> + <bcf:map> + <bcf:per_type>music</bcf:per_type> + <bcf:map_step map_field_source="addendum" map_notmatch="mkbibemph" map_final="1"/> + <bcf:map_step map_field_source="addendum" map_match="(.+)\s+app$" map_replace="\AddToHookNext {para/begin}{\box_gclear:N \g_para_indent_box }\@centercr mkbibemph\{$1\} app"/> + </bcf:map> + <bcf:map> + <bcf:per_type>audio</bcf:per_type> + <bcf:map_step map_field_source="addendum" map_notmatch="mkbibemph" map_final="1"/> + <bcf:map_step map_field_source="addendum" map_match="(.+)\s+app$" map_replace="\AddToHookNext {para/begin}{\box_gclear:N \g_para_indent_box }\@centercr mkbibemph\{$1\} app"/> + </bcf:map> + <bcf:map> + <bcf:per_type>software</bcf:per_type> + <bcf:map_step map_field_source="maintitle" map_notmatch="mkbibemph" map_final="1"/> + <bcf:map_step map_field_source="maintitle" map_match="(.+)\s+app$" map_replace="$1 \AddToHookNext {para/begin}{\box_gclear:N \g_para_indent_box }\@centercr mkbibemph\{app\}"/> + </bcf:map> + <bcf:map> + <bcf:per_type>music</bcf:per_type> + <bcf:map_step map_notfield="title" map_final="1"/> + <bcf:map_step map_field_source="booktitle" map_match="(.+)" map_final="1"/> + <bcf:map_step map_field_set="title" map_field_value="$1" map_final="1"/> + <bcf:map_step map_field_set="booktitle" map_null="1"/> + <bcf:map_step map_field_set="entrysubtype" map_field_value="album"/> + </bcf:map> + <bcf:map> + <bcf:per_type>patent</bcf:per_type> + <bcf:map_step map_notfield="publisher" map_final="1"/> + <bcf:map_step map_field_source="type" map_match="patentus" map_final="1"/> + <bcf:map_step map_field_set="publisher" map_field_value="United States Patent and Trademark Office"/> + </bcf:map> + <bcf:map map_overwrite="1"> + <bcf:map_step map_field_source="edition" map_match="edition" map_replace="ed."/> + </bcf:map> + <bcf:map map_overwrite="1"> + <bcf:map_step map_field_source="publisher" map_match="and Company" map_replace=""/> + <bcf:map_step map_field_source="publisher" map_match="and Co." map_replace=""/> + </bcf:map> + <bcf:map> + <bcf:map_step map_field_source="publisher" map_match="University Press" map_replace="UP"/> + <bcf:map_step map_field_source="publisher" map_match="University" map_replace="U"/> + <bcf:map_step map_field_source="publisher" map_match="Press\b" map_replace="P"/> + <bcf:map_step map_field_source="publisher" map_match="Corporation|Corp.|Incorporated|Inc.|Limited|Ltd." map_replace=""/> + </bcf:map> + <bcf:map> + <bcf:map_step map_field_source="institution" map_match="University" map_replace="U"/> + <bcf:map_step map_field_source="school" map_match="University" map_replace="U"/> + </bcf:map> + <bcf:map> + <bcf:map_step map_field_source="url" map_match="jstor.org" map_final="1"/> + <bcf:map_step map_field_set="eprint" map_field_value="JSTOR"/> + </bcf:map> + <bcf:map> + <bcf:map_step map_field_source="url" map_match="muse.jhu.edu" map_final="1"/> + <bcf:map_step map_field_set="eprint" map_field_value="Project Muse"/> + </bcf:map> + <bcf:map> + <bcf:map_step map_field_source="url" map_match="ebooks.adelaide.edu.au" map_final="1"/> + <bcf:map_step map_field_set="eprint" map_origfieldval="1"/> + <bcf:map_step map_field_set="eprinttype" map_field_value="adelaide"/> + </bcf:map> + <bcf:map> + <bcf:map_step map_field_source="url" map_match="books.google" map_final="1"/> + <bcf:map_step map_field_set="eprint" map_field_value="Google Books"/> + </bcf:map> + <bcf:map> + <bcf:map_step map_field_source="url" map_match="db=a9h" map_final="1"/> + <bcf:map_step map_field_set="eprint" map_field_value="Academic Search Complete"/> + </bcf:map> + <bcf:map> + <bcf:map_step map_field_source="url" map_match="db=fdcaae48" map_final="1"/> + <bcf:map_step map_field_set="eprint" map_field_value="LexisNexis Academic"/> + </bcf:map> + <bcf:map> + <bcf:map_step map_field_source="url" map_match="db=mzh" map_final="1"/> + <bcf:map_step map_field_set="eprint" map_field_value="MLA International Bibliography"/> + </bcf:map> + <bcf:map> + <bcf:map_step map_field_source="url" map_match="patft.uspto.gov" map_final="1"/> + <bcf:map_step map_field_set="eprint" map_field_value="USPTO Patent Full-Text and Image Database"/> + </bcf:map> + <bcf:map> + <bcf:map_step map_field_source="url" map_match="dx.doi.org/(.+)" map_field_target="doi"/> + <bcf:map_step map_field_source="doi" map_match="http(s)?://dx.doi.org/(.+)" map_replace="$1"/> + <bcf:map_step map_field_source="doi" map_match="dx.doi.org/(.+)" map_replace="$1"/> + </bcf:map> + <bcf:map> + <bcf:map_step map_field_source="isbn" map_final="1"/> + <bcf:map_step map_field_set="isbn" map_null="1"/> + </bcf:map> + <bcf:map> + <bcf:map_step map_field_source="doi" map_final="1"/> + <bcf:map_step map_field_set="url" map_null="1"/> + <bcf:map_step map_field_set="urldate" map_null="1"/> + </bcf:map> + <bcf:map map_overwrite="1"> + <bcf:map_step map_field_source="url" map_match="http(s)?://" map_replace=""/> + </bcf:map> + </bcf:maps> + <bcf:maps datatype="bibtex" level="driver"> + <bcf:map> + <bcf:map_step map_field_set="day" map_null="1"/> + </bcf:map> + <bcf:map> + <bcf:map_step map_type_source="conference" map_type_target="inproceedings"/> + <bcf:map_step map_type_source="electronic" map_type_target="online"/> + <bcf:map_step map_type_source="www" map_type_target="online"/> + </bcf:map> + <bcf:map> + <bcf:map_step map_type_source="mastersthesis" map_type_target="thesis" map_final="1"/> + <bcf:map_step map_field_set="type" map_field_value="mathesis"/> + </bcf:map> + <bcf:map> + <bcf:map_step map_type_source="phdthesis" map_type_target="thesis" map_final="1"/> + <bcf:map_step map_field_set="type" map_field_value="phdthesis"/> + </bcf:map> + <bcf:map> + <bcf:map_step map_type_source="techreport" map_type_target="report" map_final="1"/> + <bcf:map_step map_field_set="type" map_field_value="techreport"/> + </bcf:map> + <bcf:map> + <bcf:map_step map_field_source="hyphenation" map_field_target="langid"/> + <bcf:map_step map_field_source="address" map_field_target="location"/> + <bcf:map_step map_field_source="school" map_field_target="institution"/> + <bcf:map_step map_field_source="annote" map_field_target="annotation"/> + <bcf:map_step map_field_source="archiveprefix" map_field_target="eprinttype"/> + <bcf:map_step map_field_source="journal" map_field_target="journaltitle"/> + <bcf:map_step map_field_source="primaryclass" map_field_target="eprintclass"/> + <bcf:map_step map_field_source="key" map_field_target="sortkey"/> + <bcf:map_step map_field_source="pdf" map_field_target="file"/> + </bcf:map> + </bcf:maps> + </bcf:sourcemap> + <!-- LABELALPHA NAME TEMPLATE --> + <bcf:labelalphanametemplate name="global"> + <bcf:namepart order="1" use="1" pre="1" substring_width="1" substring_compound="1">prefix</bcf:namepart> + <bcf:namepart order="2">family</bcf:namepart> + </bcf:labelalphanametemplate> + <!-- LABELALPHA TEMPLATE --> + <bcf:labelalphatemplate type="global"> + <bcf:labelelement order="1"> + <bcf:labelpart final="1">shorthand</bcf:labelpart> + <bcf:labelpart>label</bcf:labelpart> + <bcf:labelpart substring_width="3" substring_side="left" ifnames="1">labelname</bcf:labelpart> + <bcf:labelpart substring_width="1" substring_side="left">labelname</bcf:labelpart> + </bcf:labelelement> + <bcf:labelelement order="2"> + <bcf:labelpart substring_width="2" substring_side="right">year</bcf:labelpart> + </bcf:labelelement> + </bcf:labelalphatemplate> + <!-- EXTRADATE --> + <bcf:extradatespec> + <bcf:scope> + <bcf:field order="1">labelyear</bcf:field> + <bcf:field order="2">year</bcf:field> + </bcf:scope> + </bcf:extradatespec> + <!-- INHERITANCE --> + <bcf:inheritance> + <bcf:defaults inherit_all="true" override_target="false"> + </bcf:defaults> + <bcf:inherit> + <bcf:type_pair source="mvbook" target="inbook"/> + <bcf:type_pair source="mvbook" target="bookinbook"/> + <bcf:type_pair source="mvbook" target="suppbook"/> + <bcf:type_pair source="book" target="inbook"/> + <bcf:type_pair source="book" target="bookinbook"/> + <bcf:type_pair source="book" target="suppbook"/> + <bcf:field source="author" target="author"/> + <bcf:field source="author" target="bookauthor"/> + </bcf:inherit> + <bcf:inherit> + <bcf:type_pair source="mvbook" target="book"/> + <bcf:type_pair source="mvbook" target="inbook"/> + <bcf:type_pair source="mvbook" target="bookinbook"/> + <bcf:type_pair source="mvbook" target="suppbook"/> + <bcf:field source="title" target="maintitle"/> + <bcf:field source="subtitle" target="mainsubtitle"/> + <bcf:field source="titleaddon" target="maintitleaddon"/> + <bcf:field source="shorttitle" skip="true"/> + <bcf:field source="sorttitle" skip="true"/> + <bcf:field source="indextitle" skip="true"/> + <bcf:field source="indexsorttitle" skip="true"/> + </bcf:inherit> + <bcf:inherit> + <bcf:type_pair source="mvcollection" target="collection"/> + <bcf:type_pair source="mvcollection" target="reference"/> + <bcf:type_pair source="mvcollection" target="incollection"/> + <bcf:type_pair source="mvcollection" target="inreference"/> + <bcf:type_pair source="mvcollection" target="suppcollection"/> + <bcf:type_pair source="mvreference" target="collection"/> + <bcf:type_pair source="mvreference" target="reference"/> + <bcf:type_pair source="mvreference" target="incollection"/> + <bcf:type_pair source="mvreference" target="inreference"/> + <bcf:type_pair source="mvreference" target="suppcollection"/> + <bcf:field source="title" target="maintitle"/> + <bcf:field source="subtitle" target="mainsubtitle"/> + <bcf:field source="titleaddon" target="maintitleaddon"/> + <bcf:field source="shorttitle" skip="true"/> + <bcf:field source="sorttitle" skip="true"/> + <bcf:field source="indextitle" skip="true"/> + <bcf:field source="indexsorttitle" skip="true"/> + </bcf:inherit> + <bcf:inherit> + <bcf:type_pair source="mvproceedings" target="proceedings"/> + <bcf:type_pair source="mvproceedings" target="inproceedings"/> + <bcf:field source="title" target="maintitle"/> + <bcf:field source="subtitle" target="mainsubtitle"/> + <bcf:field source="titleaddon" target="maintitleaddon"/> + <bcf:field source="shorttitle" skip="true"/> + <bcf:field source="sorttitle" skip="true"/> + <bcf:field source="indextitle" skip="true"/> + <bcf:field source="indexsorttitle" skip="true"/> + </bcf:inherit> + <bcf:inherit> + <bcf:type_pair source="book" target="inbook"/> + <bcf:type_pair source="book" target="bookinbook"/> + <bcf:type_pair source="book" target="suppbook"/> + <bcf:field source="title" target="booktitle"/> + <bcf:field source="subtitle" target="booksubtitle"/> + <bcf:field source="titleaddon" target="booktitleaddon"/> + <bcf:field source="shorttitle" skip="true"/> + <bcf:field source="sorttitle" skip="true"/> + <bcf:field source="indextitle" skip="true"/> + <bcf:field source="indexsorttitle" skip="true"/> + </bcf:inherit> + <bcf:inherit> + <bcf:type_pair source="collection" target="incollection"/> + <bcf:type_pair source="collection" target="inreference"/> + <bcf:type_pair source="collection" target="suppcollection"/> + <bcf:type_pair source="reference" target="incollection"/> + <bcf:type_pair source="reference" target="inreference"/> + <bcf:type_pair source="reference" target="suppcollection"/> + <bcf:field source="title" target="booktitle"/> + <bcf:field source="subtitle" target="booksubtitle"/> + <bcf:field source="titleaddon" target="booktitleaddon"/> + <bcf:field source="shorttitle" skip="true"/> + <bcf:field source="sorttitle" skip="true"/> + <bcf:field source="indextitle" skip="true"/> + <bcf:field source="indexsorttitle" skip="true"/> + </bcf:inherit> + <bcf:inherit> + <bcf:type_pair source="proceedings" target="inproceedings"/> + <bcf:field source="title" target="booktitle"/> + <bcf:field source="subtitle" target="booksubtitle"/> + <bcf:field source="titleaddon" target="booktitleaddon"/> + <bcf:field source="shorttitle" skip="true"/> + <bcf:field source="sorttitle" skip="true"/> + <bcf:field source="indextitle" skip="true"/> + <bcf:field source="indexsorttitle" skip="true"/> + </bcf:inherit> + <bcf:inherit> + <bcf:type_pair source="periodical" target="article"/> + <bcf:type_pair source="periodical" target="suppperiodical"/> + <bcf:field source="title" target="journaltitle"/> + <bcf:field source="subtitle" target="journalsubtitle"/> + <bcf:field source="titleaddon" target="journaltitleaddon"/> + <bcf:field source="shorttitle" skip="true"/> + <bcf:field source="sorttitle" skip="true"/> + <bcf:field source="indextitle" skip="true"/> + <bcf:field source="indexsorttitle" skip="true"/> + </bcf:inherit> + <bcf:inherit> + <bcf:type_pair source="*" target="*"/> + <bcf:field source="ids" skip="true"/> + <bcf:field source="crossref" skip="true"/> + <bcf:field source="xref" skip="true"/> + <bcf:field source="entryset" skip="true"/> + <bcf:field source="entrysubtype" skip="true"/> + <bcf:field source="execute" skip="true"/> + <bcf:field source="label" skip="true"/> + <bcf:field source="options" skip="true"/> + <bcf:field source="presort" skip="true"/> + <bcf:field source="related" skip="true"/> + <bcf:field source="relatedoptions" skip="true"/> + <bcf:field source="relatedstring" skip="true"/> + <bcf:field source="relatedtype" skip="true"/> + <bcf:field source="shorthand" skip="true"/> + <bcf:field source="shorthandintro" skip="true"/> + <bcf:field source="sortkey" skip="true"/> + </bcf:inherit> + </bcf:inheritance> + <!-- UNIQUENAME TEMPLATES --> + <bcf:uniquenametemplate name="global"> + <bcf:namepart order="1" use="1" base="1">prefix</bcf:namepart> + <bcf:namepart order="2" base="1">family</bcf:namepart> + <bcf:namepart order="3">given</bcf:namepart> + </bcf:uniquenametemplate> + <!-- SORTING NAME KEY TEMPLATES --> + <bcf:sortingnamekeytemplate name="global" visibility="sort"> + <bcf:keypart order="1"> + <bcf:part type="namepart" order="1" use="1">prefix</bcf:part> + <bcf:part type="namepart" order="2">family</bcf:part> + </bcf:keypart> + <bcf:keypart order="2"> + <bcf:part type="namepart" order="1">given</bcf:part> + </bcf:keypart> + <bcf:keypart order="3"> + <bcf:part type="namepart" order="1">suffix</bcf:part> + </bcf:keypart> + <bcf:keypart order="4"> + <bcf:part type="namepart" order="1" use="0">prefix</bcf:part> + </bcf:keypart> + </bcf:sortingnamekeytemplate> + <bcf:presort>mm</bcf:presort> + <!-- DATA MODEL --> + <bcf:datamodel> + <bcf:constants> + <bcf:constant type="list" name="gender">sf,sm,sn,pf,pm,pn,pp</bcf:constant> + <bcf:constant type="list" name="nameparts">family,given,prefix,suffix</bcf:constant> + <bcf:constant type="list" name="optiondatatypes">boolean,integer,string,xml</bcf:constant> + <bcf:constant type="list" name="multiscriptforms">default,transliteration,transcription,translation</bcf:constant> + </bcf:constants> + <bcf:entrytypes> + <bcf:entrytype>article</bcf:entrytype> + <bcf:entrytype>artwork</bcf:entrytype> + <bcf:entrytype>audio</bcf:entrytype> + <bcf:entrytype>bibnote</bcf:entrytype> + <bcf:entrytype>book</bcf:entrytype> + <bcf:entrytype>bookinbook</bcf:entrytype> + <bcf:entrytype>booklet</bcf:entrytype> + <bcf:entrytype>collection</bcf:entrytype> + <bcf:entrytype>commentary</bcf:entrytype> + <bcf:entrytype>customa</bcf:entrytype> + <bcf:entrytype>customb</bcf:entrytype> + <bcf:entrytype>customc</bcf:entrytype> + <bcf:entrytype>customd</bcf:entrytype> + <bcf:entrytype>custome</bcf:entrytype> + <bcf:entrytype>customf</bcf:entrytype> + <bcf:entrytype>dataset</bcf:entrytype> + <bcf:entrytype>inbook</bcf:entrytype> + <bcf:entrytype>incollection</bcf:entrytype> + <bcf:entrytype>inproceedings</bcf:entrytype> + <bcf:entrytype>inreference</bcf:entrytype> + <bcf:entrytype>image</bcf:entrytype> + <bcf:entrytype>jurisdiction</bcf:entrytype> + <bcf:entrytype>legal</bcf:entrytype> + <bcf:entrytype>legislation</bcf:entrytype> + <bcf:entrytype>letter</bcf:entrytype> + <bcf:entrytype>manual</bcf:entrytype> + <bcf:entrytype>misc</bcf:entrytype> + <bcf:entrytype>movie</bcf:entrytype> + <bcf:entrytype>music</bcf:entrytype> + <bcf:entrytype>mvcollection</bcf:entrytype> + <bcf:entrytype>mvreference</bcf:entrytype> + <bcf:entrytype>mvproceedings</bcf:entrytype> + <bcf:entrytype>mvbook</bcf:entrytype> + <bcf:entrytype>online</bcf:entrytype> + <bcf:entrytype>patent</bcf:entrytype> + <bcf:entrytype>performance</bcf:entrytype> + <bcf:entrytype>periodical</bcf:entrytype> + <bcf:entrytype>proceedings</bcf:entrytype> + <bcf:entrytype>reference</bcf:entrytype> + <bcf:entrytype>report</bcf:entrytype> + <bcf:entrytype>review</bcf:entrytype> + <bcf:entrytype>set</bcf:entrytype> + <bcf:entrytype>software</bcf:entrytype> + <bcf:entrytype>standard</bcf:entrytype> + <bcf:entrytype>suppbook</bcf:entrytype> + <bcf:entrytype>suppcollection</bcf:entrytype> + <bcf:entrytype>suppperiodical</bcf:entrytype> + <bcf:entrytype>thesis</bcf:entrytype> + <bcf:entrytype>unpublished</bcf:entrytype> + <bcf:entrytype>video</bcf:entrytype> + <bcf:entrytype skip_output="true">xdata</bcf:entrytype> + </bcf:entrytypes> + <bcf:fields> + <bcf:field fieldtype="field" datatype="integer">sortyear</bcf:field> + <bcf:field fieldtype="field" datatype="integer">volume</bcf:field> + <bcf:field fieldtype="field" datatype="integer">volumes</bcf:field> + <bcf:field fieldtype="field" datatype="literal">abstract</bcf:field> + <bcf:field fieldtype="field" datatype="literal">addendum</bcf:field> + <bcf:field fieldtype="field" datatype="literal">annotation</bcf:field> + <bcf:field fieldtype="field" datatype="literal">booksubtitle</bcf:field> + <bcf:field fieldtype="field" datatype="literal">booktitle</bcf:field> + <bcf:field fieldtype="field" datatype="literal">booktitleaddon</bcf:field> + <bcf:field fieldtype="field" datatype="literal">chapter</bcf:field> + <bcf:field fieldtype="field" datatype="literal">edition</bcf:field> + <bcf:field fieldtype="field" datatype="literal">eid</bcf:field> + <bcf:field fieldtype="field" datatype="literal">entrysubtype</bcf:field> + <bcf:field fieldtype="field" datatype="literal">eprintclass</bcf:field> + <bcf:field fieldtype="field" datatype="literal">eprinttype</bcf:field> + <bcf:field fieldtype="field" datatype="literal">eventtitle</bcf:field> + <bcf:field fieldtype="field" datatype="literal">eventtitleaddon</bcf:field> + <bcf:field fieldtype="field" datatype="literal">gender</bcf:field> + <bcf:field fieldtype="field" datatype="literal">howpublished</bcf:field> + <bcf:field fieldtype="field" datatype="literal">indexsorttitle</bcf:field> + <bcf:field fieldtype="field" datatype="literal">indextitle</bcf:field> + <bcf:field fieldtype="field" datatype="literal">isan</bcf:field> + <bcf:field fieldtype="field" datatype="literal">isbn</bcf:field> + <bcf:field fieldtype="field" datatype="literal">ismn</bcf:field> + <bcf:field fieldtype="field" datatype="literal">isrn</bcf:field> + <bcf:field fieldtype="field" datatype="literal">issn</bcf:field> + <bcf:field fieldtype="field" datatype="literal">issue</bcf:field> + <bcf:field fieldtype="field" datatype="literal">issuesubtitle</bcf:field> + <bcf:field fieldtype="field" datatype="literal">issuetitle</bcf:field> + <bcf:field fieldtype="field" datatype="literal">issuetitleaddon</bcf:field> + <bcf:field fieldtype="field" datatype="literal">iswc</bcf:field> + <bcf:field fieldtype="field" datatype="literal">journalsubtitle</bcf:field> + <bcf:field fieldtype="field" datatype="literal">journaltitle</bcf:field> + <bcf:field fieldtype="field" datatype="literal">journaltitleaddon</bcf:field> + <bcf:field fieldtype="field" datatype="literal">label</bcf:field> + <bcf:field fieldtype="field" datatype="literal">langid</bcf:field> + <bcf:field fieldtype="field" datatype="literal">langidopts</bcf:field> + <bcf:field fieldtype="field" datatype="literal">library</bcf:field> + <bcf:field fieldtype="field" datatype="literal">mainsubtitle</bcf:field> + <bcf:field fieldtype="field" datatype="literal">maintitle</bcf:field> + <bcf:field fieldtype="field" datatype="literal">maintitleaddon</bcf:field> + <bcf:field fieldtype="field" datatype="literal">nameaddon</bcf:field> + <bcf:field fieldtype="field" datatype="literal">note</bcf:field> + <bcf:field fieldtype="field" datatype="literal">number</bcf:field> + <bcf:field fieldtype="field" datatype="literal">origtitle</bcf:field> + <bcf:field fieldtype="field" datatype="literal">pagetotal</bcf:field> + <bcf:field fieldtype="field" datatype="literal">part</bcf:field> + <bcf:field fieldtype="field" datatype="literal">relatedstring</bcf:field> + <bcf:field fieldtype="field" datatype="literal">relatedtype</bcf:field> + <bcf:field fieldtype="field" datatype="literal">reprinttitle</bcf:field> + <bcf:field fieldtype="field" datatype="literal">series</bcf:field> + <bcf:field fieldtype="field" datatype="literal">shorthandintro</bcf:field> + <bcf:field fieldtype="field" datatype="literal">subtitle</bcf:field> + <bcf:field fieldtype="field" datatype="literal">title</bcf:field> + <bcf:field fieldtype="field" datatype="literal">titleaddon</bcf:field> + <bcf:field fieldtype="field" datatype="literal">usera</bcf:field> + <bcf:field fieldtype="field" datatype="literal">userb</bcf:field> + <bcf:field fieldtype="field" datatype="literal">userc</bcf:field> + <bcf:field fieldtype="field" datatype="literal">userd</bcf:field> + <bcf:field fieldtype="field" datatype="literal">usere</bcf:field> + <bcf:field fieldtype="field" datatype="literal">userf</bcf:field> + <bcf:field fieldtype="field" datatype="literal">venue</bcf:field> + <bcf:field fieldtype="field" datatype="literal">version</bcf:field> + <bcf:field fieldtype="field" datatype="literal" label="true">shorthand</bcf:field> + <bcf:field fieldtype="field" datatype="literal" label="true">shortjournal</bcf:field> + <bcf:field fieldtype="field" datatype="literal" label="true">shortseries</bcf:field> + <bcf:field fieldtype="field" datatype="literal" label="true">shorttitle</bcf:field> + <bcf:field fieldtype="field" datatype="literal" skip_output="true">sorttitle</bcf:field> + <bcf:field fieldtype="field" datatype="literal" skip_output="true">sortshorthand</bcf:field> + <bcf:field fieldtype="field" datatype="literal" skip_output="true">sortkey</bcf:field> + <bcf:field fieldtype="field" datatype="literal" skip_output="true">presort</bcf:field> + <bcf:field fieldtype="list" datatype="literal">institution</bcf:field> + <bcf:field fieldtype="list" datatype="literal">lista</bcf:field> + <bcf:field fieldtype="list" datatype="literal">listb</bcf:field> + <bcf:field fieldtype="list" datatype="literal">listc</bcf:field> + <bcf:field fieldtype="list" datatype="literal">listd</bcf:field> + <bcf:field fieldtype="list" datatype="literal">liste</bcf:field> + <bcf:field fieldtype="list" datatype="literal">listf</bcf:field> + <bcf:field fieldtype="list" datatype="literal">location</bcf:field> + <bcf:field fieldtype="list" datatype="literal">organization</bcf:field> + <bcf:field fieldtype="list" datatype="literal">origlocation</bcf:field> + <bcf:field fieldtype="list" datatype="literal">origpublisher</bcf:field> + <bcf:field fieldtype="list" datatype="literal">publisher</bcf:field> + <bcf:field fieldtype="list" datatype="name">afterword</bcf:field> + <bcf:field fieldtype="list" datatype="name">annotator</bcf:field> + <bcf:field fieldtype="list" datatype="name">author</bcf:field> + <bcf:field fieldtype="list" datatype="name">bookauthor</bcf:field> + <bcf:field fieldtype="list" datatype="name">commentator</bcf:field> + <bcf:field fieldtype="list" datatype="name">editor</bcf:field> + <bcf:field fieldtype="list" datatype="name">editora</bcf:field> + <bcf:field fieldtype="list" datatype="name">editorb</bcf:field> + <bcf:field fieldtype="list" datatype="name">editorc</bcf:field> + <bcf:field fieldtype="list" datatype="name">foreword</bcf:field> + <bcf:field fieldtype="list" datatype="name">holder</bcf:field> + <bcf:field fieldtype="list" datatype="name">introduction</bcf:field> + <bcf:field fieldtype="list" datatype="name">namea</bcf:field> + <bcf:field fieldtype="list" datatype="name">nameb</bcf:field> + <bcf:field fieldtype="list" datatype="name">namec</bcf:field> + <bcf:field fieldtype="list" datatype="name">translator</bcf:field> + <bcf:field fieldtype="list" datatype="name" label="true">shortauthor</bcf:field> + <bcf:field fieldtype="list" datatype="name" label="true">shorteditor</bcf:field> + <bcf:field fieldtype="list" datatype="name" skip_output="true">sortname</bcf:field> + <bcf:field fieldtype="field" datatype="key">authortype</bcf:field> + <bcf:field fieldtype="field" datatype="key">editoratype</bcf:field> + <bcf:field fieldtype="field" datatype="key">editorbtype</bcf:field> + <bcf:field fieldtype="field" datatype="key">editorctype</bcf:field> + <bcf:field fieldtype="field" datatype="key">editortype</bcf:field> + <bcf:field fieldtype="field" datatype="key">bookpagination</bcf:field> + <bcf:field fieldtype="field" datatype="key">nameatype</bcf:field> + <bcf:field fieldtype="field" datatype="key">namebtype</bcf:field> + <bcf:field fieldtype="field" datatype="key">namectype</bcf:field> + <bcf:field fieldtype="field" datatype="key">pagination</bcf:field> + <bcf:field fieldtype="field" datatype="key">pubstate</bcf:field> + <bcf:field fieldtype="field" datatype="key">type</bcf:field> + <bcf:field fieldtype="list" datatype="key">language</bcf:field> + <bcf:field fieldtype="list" datatype="key">origlanguage</bcf:field> + <bcf:field fieldtype="field" datatype="entrykey">crossref</bcf:field> + <bcf:field fieldtype="field" datatype="entrykey">xref</bcf:field> + <bcf:field fieldtype="field" datatype="date" skip_output="true">date</bcf:field> + <bcf:field fieldtype="field" datatype="datepart" nullok="true">endyear</bcf:field> + <bcf:field fieldtype="field" datatype="datepart" nullok="true">year</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">month</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">day</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">hour</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">minute</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">second</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">timezone</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">yeardivision</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">endmonth</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">endday</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">endhour</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">endminute</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">endsecond</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">endtimezone</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">endyeardivision</bcf:field> + <bcf:field fieldtype="field" datatype="date" skip_output="true">eventdate</bcf:field> + <bcf:field fieldtype="field" datatype="datepart" nullok="true">eventendyear</bcf:field> + <bcf:field fieldtype="field" datatype="datepart" nullok="true">eventyear</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">eventmonth</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">eventday</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">eventhour</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">eventminute</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">eventsecond</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">eventtimezone</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">eventyeardivision</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">eventendmonth</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">eventendday</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">eventendhour</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">eventendminute</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">eventendsecond</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">eventendtimezone</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">eventendyeardivision</bcf:field> + <bcf:field fieldtype="field" datatype="date" skip_output="true">origdate</bcf:field> + <bcf:field fieldtype="field" datatype="datepart" nullok="true">origendyear</bcf:field> + <bcf:field fieldtype="field" datatype="datepart" nullok="true">origyear</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">origmonth</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">origday</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">orighour</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">origminute</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">origsecond</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">origtimezone</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">origyeardivision</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">origendmonth</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">origendday</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">origendhour</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">origendminute</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">origendsecond</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">origendtimezone</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">origendyeardivision</bcf:field> + <bcf:field fieldtype="field" datatype="date" skip_output="true">urldate</bcf:field> + <bcf:field fieldtype="field" datatype="datepart" nullok="true">urlendyear</bcf:field> + <bcf:field fieldtype="field" datatype="datepart" nullok="true">urlyear</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">urlmonth</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">urlday</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">urlhour</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">urlminute</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">urlsecond</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">urltimezone</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">urlyeardivision</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">urlendmonth</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">urlendday</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">urlendhour</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">urlendminute</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">urlendsecond</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">urlendtimezone</bcf:field> + <bcf:field fieldtype="field" datatype="datepart">urlendyeardivision</bcf:field> + <bcf:field fieldtype="field" datatype="verbatim">doi</bcf:field> + <bcf:field fieldtype="field" datatype="verbatim">eprint</bcf:field> + <bcf:field fieldtype="field" datatype="verbatim">file</bcf:field> + <bcf:field fieldtype="field" datatype="verbatim">verba</bcf:field> + <bcf:field fieldtype="field" datatype="verbatim">verbb</bcf:field> + <bcf:field fieldtype="field" datatype="verbatim">verbc</bcf:field> + <bcf:field fieldtype="field" datatype="uri">url</bcf:field> + <bcf:field fieldtype="field" format="xsv" datatype="entrykey" skip_output="true">xdata</bcf:field> + <bcf:field fieldtype="field" format="xsv" datatype="entrykey" skip_output="true">ids</bcf:field> + <bcf:field fieldtype="field" format="xsv" datatype="entrykey" skip_output="true">entryset</bcf:field> + <bcf:field fieldtype="field" format="xsv" datatype="entrykey">related</bcf:field> + <bcf:field fieldtype="field" format="xsv" datatype="keyword">keywords</bcf:field> + <bcf:field fieldtype="field" format="xsv" datatype="option" skip_output="true">options</bcf:field> + <bcf:field fieldtype="field" format="xsv" datatype="option" skip_output="true">relatedoptions</bcf:field> + <bcf:field fieldtype="field" datatype="range">pages</bcf:field> + <bcf:field fieldtype="field" datatype="code">execute</bcf:field> + </bcf:fields> + <bcf:entryfields> + <bcf:field>abstract</bcf:field> + <bcf:field>annotation</bcf:field> + <bcf:field>authortype</bcf:field> + <bcf:field>bookpagination</bcf:field> + <bcf:field>crossref</bcf:field> + <bcf:field>day</bcf:field> + <bcf:field>doi</bcf:field> + <bcf:field>eprint</bcf:field> + <bcf:field>eprintclass</bcf:field> + <bcf:field>eprinttype</bcf:field> + <bcf:field>endday</bcf:field> + <bcf:field>endhour</bcf:field> + <bcf:field>endminute</bcf:field> + <bcf:field>endmonth</bcf:field> + <bcf:field>endsecond</bcf:field> + <bcf:field>endtimezone</bcf:field> + <bcf:field>endyear</bcf:field> + <bcf:field>endyeardivision</bcf:field> + <bcf:field>entryset</bcf:field> + <bcf:field>entrysubtype</bcf:field> + <bcf:field>execute</bcf:field> + <bcf:field>file</bcf:field> + <bcf:field>gender</bcf:field> + <bcf:field>hour</bcf:field> + <bcf:field>ids</bcf:field> + <bcf:field>indextitle</bcf:field> + <bcf:field>indexsorttitle</bcf:field> + <bcf:field>isan</bcf:field> + <bcf:field>ismn</bcf:field> + <bcf:field>iswc</bcf:field> + <bcf:field>keywords</bcf:field> + <bcf:field>label</bcf:field> + <bcf:field>langid</bcf:field> + <bcf:field>langidopts</bcf:field> + <bcf:field>library</bcf:field> + <bcf:field>lista</bcf:field> + <bcf:field>listb</bcf:field> + <bcf:field>listc</bcf:field> + <bcf:field>listd</bcf:field> + <bcf:field>liste</bcf:field> + <bcf:field>listf</bcf:field> + <bcf:field>minute</bcf:field> + <bcf:field>month</bcf:field> + <bcf:field>namea</bcf:field> + <bcf:field>nameb</bcf:field> + <bcf:field>namec</bcf:field> + <bcf:field>nameatype</bcf:field> + <bcf:field>namebtype</bcf:field> + <bcf:field>namectype</bcf:field> + <bcf:field>nameaddon</bcf:field> + <bcf:field>options</bcf:field> + <bcf:field>origday</bcf:field> + <bcf:field>origendday</bcf:field> + <bcf:field>origendhour</bcf:field> + <bcf:field>origendminute</bcf:field> + <bcf:field>origendmonth</bcf:field> + <bcf:field>origendsecond</bcf:field> + <bcf:field>origendtimezone</bcf:field> + <bcf:field>origendyear</bcf:field> + <bcf:field>origendyeardivision</bcf:field> + <bcf:field>orighour</bcf:field> + <bcf:field>origminute</bcf:field> + <bcf:field>origmonth</bcf:field> + <bcf:field>origsecond</bcf:field> + <bcf:field>origtimezone</bcf:field> + <bcf:field>origyear</bcf:field> + <bcf:field>origyeardivision</bcf:field> + <bcf:field>origlocation</bcf:field> + <bcf:field>origpublisher</bcf:field> + <bcf:field>origtitle</bcf:field> + <bcf:field>pagination</bcf:field> + <bcf:field>presort</bcf:field> + <bcf:field>related</bcf:field> + <bcf:field>relatedoptions</bcf:field> + <bcf:field>relatedstring</bcf:field> + <bcf:field>relatedtype</bcf:field> + <bcf:field>second</bcf:field> + <bcf:field>shortauthor</bcf:field> + <bcf:field>shorteditor</bcf:field> + <bcf:field>shorthand</bcf:field> + <bcf:field>shorthandintro</bcf:field> + <bcf:field>shortjournal</bcf:field> + <bcf:field>shortseries</bcf:field> + <bcf:field>shorttitle</bcf:field> + <bcf:field>sortkey</bcf:field> + <bcf:field>sortname</bcf:field> + <bcf:field>sortshorthand</bcf:field> + <bcf:field>sorttitle</bcf:field> + <bcf:field>sortyear</bcf:field> + <bcf:field>timezone</bcf:field> + <bcf:field>url</bcf:field> + <bcf:field>urlday</bcf:field> + <bcf:field>urlendday</bcf:field> + <bcf:field>urlendhour</bcf:field> + <bcf:field>urlendminute</bcf:field> + <bcf:field>urlendmonth</bcf:field> + <bcf:field>urlendsecond</bcf:field> + <bcf:field>urlendtimezone</bcf:field> + <bcf:field>urlendyear</bcf:field> + <bcf:field>urlhour</bcf:field> + <bcf:field>urlminute</bcf:field> + <bcf:field>urlmonth</bcf:field> + <bcf:field>urlsecond</bcf:field> + <bcf:field>urltimezone</bcf:field> + <bcf:field>urlyear</bcf:field> + <bcf:field>usera</bcf:field> + <bcf:field>userb</bcf:field> + <bcf:field>userc</bcf:field> + <bcf:field>userd</bcf:field> + <bcf:field>usere</bcf:field> + <bcf:field>userf</bcf:field> + <bcf:field>verba</bcf:field> + <bcf:field>verbb</bcf:field> + <bcf:field>verbc</bcf:field> + <bcf:field>xdata</bcf:field> + <bcf:field>xref</bcf:field> + <bcf:field>year</bcf:field> + <bcf:field>yeardivision</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>set</bcf:entrytype> + <bcf:field>entryset</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>article</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>annotator</bcf:field> + <bcf:field>author</bcf:field> + <bcf:field>commentator</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editora</bcf:field> + <bcf:field>editorb</bcf:field> + <bcf:field>editorc</bcf:field> + <bcf:field>editortype</bcf:field> + <bcf:field>editoratype</bcf:field> + <bcf:field>editorbtype</bcf:field> + <bcf:field>editorctype</bcf:field> + <bcf:field>eid</bcf:field> + <bcf:field>issn</bcf:field> + <bcf:field>issue</bcf:field> + <bcf:field>issuetitle</bcf:field> + <bcf:field>issuesubtitle</bcf:field> + <bcf:field>issuetitleaddon</bcf:field> + <bcf:field>journalsubtitle</bcf:field> + <bcf:field>journaltitle</bcf:field> + <bcf:field>journaltitleaddon</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>number</bcf:field> + <bcf:field>origlanguage</bcf:field> + <bcf:field>pages</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>series</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>translator</bcf:field> + <bcf:field>version</bcf:field> + <bcf:field>volume</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>bibnote</bcf:entrytype> + <bcf:field>note</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>book</bcf:entrytype> + <bcf:field>author</bcf:field> + <bcf:field>addendum</bcf:field> + <bcf:field>afterword</bcf:field> + <bcf:field>annotator</bcf:field> + <bcf:field>chapter</bcf:field> + <bcf:field>commentator</bcf:field> + <bcf:field>edition</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editora</bcf:field> + <bcf:field>editorb</bcf:field> + <bcf:field>editorc</bcf:field> + <bcf:field>editortype</bcf:field> + <bcf:field>editoratype</bcf:field> + <bcf:field>editorbtype</bcf:field> + <bcf:field>editorctype</bcf:field> + <bcf:field>eid</bcf:field> + <bcf:field>foreword</bcf:field> + <bcf:field>introduction</bcf:field> + <bcf:field>isbn</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>maintitle</bcf:field> + <bcf:field>maintitleaddon</bcf:field> + <bcf:field>mainsubtitle</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>number</bcf:field> + <bcf:field>origlanguage</bcf:field> + <bcf:field>pages</bcf:field> + <bcf:field>pagetotal</bcf:field> + <bcf:field>part</bcf:field> + <bcf:field>publisher</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>series</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>translator</bcf:field> + <bcf:field>volume</bcf:field> + <bcf:field>volumes</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>mvbook</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>afterword</bcf:field> + <bcf:field>annotator</bcf:field> + <bcf:field>author</bcf:field> + <bcf:field>commentator</bcf:field> + <bcf:field>edition</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editora</bcf:field> + <bcf:field>editorb</bcf:field> + <bcf:field>editorc</bcf:field> + <bcf:field>editortype</bcf:field> + <bcf:field>editoratype</bcf:field> + <bcf:field>editorbtype</bcf:field> + <bcf:field>editorctype</bcf:field> + <bcf:field>foreword</bcf:field> + <bcf:field>introduction</bcf:field> + <bcf:field>isbn</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>number</bcf:field> + <bcf:field>origlanguage</bcf:field> + <bcf:field>pagetotal</bcf:field> + <bcf:field>publisher</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>series</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>translator</bcf:field> + <bcf:field>volume</bcf:field> + <bcf:field>volumes</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>inbook</bcf:entrytype> + <bcf:entrytype>bookinbook</bcf:entrytype> + <bcf:entrytype>suppbook</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>afterword</bcf:field> + <bcf:field>annotator</bcf:field> + <bcf:field>author</bcf:field> + <bcf:field>booktitle</bcf:field> + <bcf:field>bookauthor</bcf:field> + <bcf:field>booksubtitle</bcf:field> + <bcf:field>booktitleaddon</bcf:field> + <bcf:field>chapter</bcf:field> + <bcf:field>commentator</bcf:field> + <bcf:field>edition</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editora</bcf:field> + <bcf:field>editorb</bcf:field> + <bcf:field>editorc</bcf:field> + <bcf:field>editortype</bcf:field> + <bcf:field>editoratype</bcf:field> + <bcf:field>editorbtype</bcf:field> + <bcf:field>editorctype</bcf:field> + <bcf:field>eid</bcf:field> + <bcf:field>foreword</bcf:field> + <bcf:field>introduction</bcf:field> + <bcf:field>isbn</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>mainsubtitle</bcf:field> + <bcf:field>maintitle</bcf:field> + <bcf:field>maintitleaddon</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>number</bcf:field> + <bcf:field>origlanguage</bcf:field> + <bcf:field>part</bcf:field> + <bcf:field>publisher</bcf:field> + <bcf:field>pages</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>series</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>translator</bcf:field> + <bcf:field>volume</bcf:field> + <bcf:field>volumes</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>booklet</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>author</bcf:field> + <bcf:field>chapter</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editortype</bcf:field> + <bcf:field>eid</bcf:field> + <bcf:field>howpublished</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>pages</bcf:field> + <bcf:field>pagetotal</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>type</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>collection</bcf:entrytype> + <bcf:entrytype>reference</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>afterword</bcf:field> + <bcf:field>annotator</bcf:field> + <bcf:field>chapter</bcf:field> + <bcf:field>commentator</bcf:field> + <bcf:field>edition</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editora</bcf:field> + <bcf:field>editorb</bcf:field> + <bcf:field>editorc</bcf:field> + <bcf:field>editortype</bcf:field> + <bcf:field>editoratype</bcf:field> + <bcf:field>editorbtype</bcf:field> + <bcf:field>editorctype</bcf:field> + <bcf:field>eid</bcf:field> + <bcf:field>foreword</bcf:field> + <bcf:field>introduction</bcf:field> + <bcf:field>isbn</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>mainsubtitle</bcf:field> + <bcf:field>maintitle</bcf:field> + <bcf:field>maintitleaddon</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>number</bcf:field> + <bcf:field>origlanguage</bcf:field> + <bcf:field>pages</bcf:field> + <bcf:field>pagetotal</bcf:field> + <bcf:field>part</bcf:field> + <bcf:field>publisher</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>series</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>translator</bcf:field> + <bcf:field>volume</bcf:field> + <bcf:field>volumes</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>mvcollection</bcf:entrytype> + <bcf:entrytype>mvreference</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>afterword</bcf:field> + <bcf:field>annotator</bcf:field> + <bcf:field>author</bcf:field> + <bcf:field>commentator</bcf:field> + <bcf:field>edition</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editora</bcf:field> + <bcf:field>editorb</bcf:field> + <bcf:field>editorc</bcf:field> + <bcf:field>editortype</bcf:field> + <bcf:field>editoratype</bcf:field> + <bcf:field>editorbtype</bcf:field> + <bcf:field>editorctype</bcf:field> + <bcf:field>foreword</bcf:field> + <bcf:field>introduction</bcf:field> + <bcf:field>isbn</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>number</bcf:field> + <bcf:field>origlanguage</bcf:field> + <bcf:field>publisher</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>translator</bcf:field> + <bcf:field>volume</bcf:field> + <bcf:field>volumes</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>incollection</bcf:entrytype> + <bcf:entrytype>suppcollection</bcf:entrytype> + <bcf:entrytype>inreference</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>afterword</bcf:field> + <bcf:field>annotator</bcf:field> + <bcf:field>author</bcf:field> + <bcf:field>booksubtitle</bcf:field> + <bcf:field>booktitle</bcf:field> + <bcf:field>booktitleaddon</bcf:field> + <bcf:field>chapter</bcf:field> + <bcf:field>commentator</bcf:field> + <bcf:field>edition</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editora</bcf:field> + <bcf:field>editorb</bcf:field> + <bcf:field>editorc</bcf:field> + <bcf:field>editortype</bcf:field> + <bcf:field>editoratype</bcf:field> + <bcf:field>editorbtype</bcf:field> + <bcf:field>editorctype</bcf:field> + <bcf:field>eid</bcf:field> + <bcf:field>foreword</bcf:field> + <bcf:field>introduction</bcf:field> + <bcf:field>isbn</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>mainsubtitle</bcf:field> + <bcf:field>maintitle</bcf:field> + <bcf:field>maintitleaddon</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>number</bcf:field> + <bcf:field>origlanguage</bcf:field> + <bcf:field>pages</bcf:field> + <bcf:field>part</bcf:field> + <bcf:field>publisher</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>series</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>translator</bcf:field> + <bcf:field>volume</bcf:field> + <bcf:field>volumes</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>dataset</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>author</bcf:field> + <bcf:field>edition</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editortype</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>number</bcf:field> + <bcf:field>organization</bcf:field> + <bcf:field>publisher</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>series</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>type</bcf:field> + <bcf:field>version</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>manual</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>author</bcf:field> + <bcf:field>chapter</bcf:field> + <bcf:field>edition</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editortype</bcf:field> + <bcf:field>eid</bcf:field> + <bcf:field>isbn</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>number</bcf:field> + <bcf:field>organization</bcf:field> + <bcf:field>pages</bcf:field> + <bcf:field>pagetotal</bcf:field> + <bcf:field>publisher</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>series</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>type</bcf:field> + <bcf:field>version</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>misc</bcf:entrytype> + <bcf:entrytype>software</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>author</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editortype</bcf:field> + <bcf:field>howpublished</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>organization</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>type</bcf:field> + <bcf:field>version</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>online</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>author</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editortype</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>organization</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>version</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>patent</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>author</bcf:field> + <bcf:field>holder</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>number</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>type</bcf:field> + <bcf:field>version</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>periodical</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editora</bcf:field> + <bcf:field>editorb</bcf:field> + <bcf:field>editorc</bcf:field> + <bcf:field>editortype</bcf:field> + <bcf:field>editoratype</bcf:field> + <bcf:field>editorbtype</bcf:field> + <bcf:field>editorctype</bcf:field> + <bcf:field>issn</bcf:field> + <bcf:field>issue</bcf:field> + <bcf:field>issuesubtitle</bcf:field> + <bcf:field>issuetitle</bcf:field> + <bcf:field>issuetitleaddon</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>number</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>series</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>volume</bcf:field> + <bcf:field>yeardivision</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>mvproceedings</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editortype</bcf:field> + <bcf:field>eventday</bcf:field> + <bcf:field>eventendday</bcf:field> + <bcf:field>eventendhour</bcf:field> + <bcf:field>eventendminute</bcf:field> + <bcf:field>eventendmonth</bcf:field> + <bcf:field>eventendsecond</bcf:field> + <bcf:field>eventendtimezone</bcf:field> + <bcf:field>eventendyear</bcf:field> + <bcf:field>eventendyeardivision</bcf:field> + <bcf:field>eventhour</bcf:field> + <bcf:field>eventminute</bcf:field> + <bcf:field>eventmonth</bcf:field> + <bcf:field>eventsecond</bcf:field> + <bcf:field>eventtimezone</bcf:field> + <bcf:field>eventyear</bcf:field> + <bcf:field>eventyeardivision</bcf:field> + <bcf:field>eventtitle</bcf:field> + <bcf:field>eventtitleaddon</bcf:field> + <bcf:field>isbn</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>number</bcf:field> + <bcf:field>organization</bcf:field> + <bcf:field>pagetotal</bcf:field> + <bcf:field>publisher</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>series</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>venue</bcf:field> + <bcf:field>volumes</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>proceedings</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>chapter</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editortype</bcf:field> + <bcf:field>eid</bcf:field> + <bcf:field>eventday</bcf:field> + <bcf:field>eventendday</bcf:field> + <bcf:field>eventendhour</bcf:field> + <bcf:field>eventendminute</bcf:field> + <bcf:field>eventendmonth</bcf:field> + <bcf:field>eventendsecond</bcf:field> + <bcf:field>eventendtimezone</bcf:field> + <bcf:field>eventendyear</bcf:field> + <bcf:field>eventendyeardivision</bcf:field> + <bcf:field>eventhour</bcf:field> + <bcf:field>eventminute</bcf:field> + <bcf:field>eventmonth</bcf:field> + <bcf:field>eventsecond</bcf:field> + <bcf:field>eventtimezone</bcf:field> + <bcf:field>eventyear</bcf:field> + <bcf:field>eventyeardivision</bcf:field> + <bcf:field>eventtitle</bcf:field> + <bcf:field>eventtitleaddon</bcf:field> + <bcf:field>isbn</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>mainsubtitle</bcf:field> + <bcf:field>maintitle</bcf:field> + <bcf:field>maintitleaddon</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>number</bcf:field> + <bcf:field>organization</bcf:field> + <bcf:field>pages</bcf:field> + <bcf:field>pagetotal</bcf:field> + <bcf:field>part</bcf:field> + <bcf:field>publisher</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>series</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>venue</bcf:field> + <bcf:field>volume</bcf:field> + <bcf:field>volumes</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>inproceedings</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>author</bcf:field> + <bcf:field>booksubtitle</bcf:field> + <bcf:field>booktitle</bcf:field> + <bcf:field>booktitleaddon</bcf:field> + <bcf:field>chapter</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editortype</bcf:field> + <bcf:field>eid</bcf:field> + <bcf:field>eventday</bcf:field> + <bcf:field>eventendday</bcf:field> + <bcf:field>eventendhour</bcf:field> + <bcf:field>eventendminute</bcf:field> + <bcf:field>eventendmonth</bcf:field> + <bcf:field>eventendsecond</bcf:field> + <bcf:field>eventendtimezone</bcf:field> + <bcf:field>eventendyear</bcf:field> + <bcf:field>eventendyeardivision</bcf:field> + <bcf:field>eventhour</bcf:field> + <bcf:field>eventminute</bcf:field> + <bcf:field>eventmonth</bcf:field> + <bcf:field>eventsecond</bcf:field> + <bcf:field>eventtimezone</bcf:field> + <bcf:field>eventyear</bcf:field> + <bcf:field>eventyeardivision</bcf:field> + <bcf:field>eventtitle</bcf:field> + <bcf:field>eventtitleaddon</bcf:field> + <bcf:field>isbn</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>mainsubtitle</bcf:field> + <bcf:field>maintitle</bcf:field> + <bcf:field>maintitleaddon</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>number</bcf:field> + <bcf:field>organization</bcf:field> + <bcf:field>pages</bcf:field> + <bcf:field>part</bcf:field> + <bcf:field>publisher</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>series</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>venue</bcf:field> + <bcf:field>volume</bcf:field> + <bcf:field>volumes</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>report</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>author</bcf:field> + <bcf:field>chapter</bcf:field> + <bcf:field>eid</bcf:field> + <bcf:field>institution</bcf:field> + <bcf:field>isrn</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>number</bcf:field> + <bcf:field>pages</bcf:field> + <bcf:field>pagetotal</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>type</bcf:field> + <bcf:field>version</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>thesis</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>author</bcf:field> + <bcf:field>chapter</bcf:field> + <bcf:field>eid</bcf:field> + <bcf:field>institution</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>pages</bcf:field> + <bcf:field>pagetotal</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>type</bcf:field> + </bcf:entryfields> + <bcf:entryfields> + <bcf:entrytype>unpublished</bcf:entrytype> + <bcf:field>addendum</bcf:field> + <bcf:field>author</bcf:field> + <bcf:field>eventday</bcf:field> + <bcf:field>eventendday</bcf:field> + <bcf:field>eventendhour</bcf:field> + <bcf:field>eventendminute</bcf:field> + <bcf:field>eventendmonth</bcf:field> + <bcf:field>eventendsecond</bcf:field> + <bcf:field>eventendtimezone</bcf:field> + <bcf:field>eventendyear</bcf:field> + <bcf:field>eventendyeardivision</bcf:field> + <bcf:field>eventhour</bcf:field> + <bcf:field>eventminute</bcf:field> + <bcf:field>eventmonth</bcf:field> + <bcf:field>eventsecond</bcf:field> + <bcf:field>eventtimezone</bcf:field> + <bcf:field>eventyear</bcf:field> + <bcf:field>eventyeardivision</bcf:field> + <bcf:field>eventtitle</bcf:field> + <bcf:field>eventtitleaddon</bcf:field> + <bcf:field>howpublished</bcf:field> + <bcf:field>language</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>pubstate</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>type</bcf:field> + <bcf:field>venue</bcf:field> + </bcf:entryfields> + <bcf:multiscriptfields> + <bcf:field>abstract</bcf:field> + <bcf:field>addendum</bcf:field> + <bcf:field>afterword</bcf:field> + <bcf:field>annotator</bcf:field> + <bcf:field>author</bcf:field> + <bcf:field>bookauthor</bcf:field> + <bcf:field>booksubtitle</bcf:field> + <bcf:field>booktitle</bcf:field> + <bcf:field>booktitleaddon</bcf:field> + <bcf:field>chapter</bcf:field> + <bcf:field>commentator</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>editora</bcf:field> + <bcf:field>editorb</bcf:field> + <bcf:field>editorc</bcf:field> + <bcf:field>foreword</bcf:field> + <bcf:field>holder</bcf:field> + <bcf:field>institution</bcf:field> + <bcf:field>introduction</bcf:field> + <bcf:field>issuesubtitle</bcf:field> + <bcf:field>issuetitle</bcf:field> + <bcf:field>issuetitleaddon</bcf:field> + <bcf:field>journalsubtitle</bcf:field> + <bcf:field>journaltitle</bcf:field> + <bcf:field>journaltitleaddon</bcf:field> + <bcf:field>location</bcf:field> + <bcf:field>mainsubtitle</bcf:field> + <bcf:field>maintitle</bcf:field> + <bcf:field>maintitleaddon</bcf:field> + <bcf:field>nameaddon</bcf:field> + <bcf:field>note</bcf:field> + <bcf:field>organization</bcf:field> + <bcf:field>origlanguage</bcf:field> + <bcf:field>origlocation</bcf:field> + <bcf:field>origpublisher</bcf:field> + <bcf:field>origtitle</bcf:field> + <bcf:field>part</bcf:field> + <bcf:field>publisher</bcf:field> + <bcf:field>relatedstring</bcf:field> + <bcf:field>series</bcf:field> + <bcf:field>shortauthor</bcf:field> + <bcf:field>shorteditor</bcf:field> + <bcf:field>shorthand</bcf:field> + <bcf:field>shortjournal</bcf:field> + <bcf:field>shortseries</bcf:field> + <bcf:field>shorttitle</bcf:field> + <bcf:field>sortname</bcf:field> + <bcf:field>sortshorthand</bcf:field> + <bcf:field>sorttitle</bcf:field> + <bcf:field>subtitle</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>titleaddon</bcf:field> + <bcf:field>translator</bcf:field> + <bcf:field>venue</bcf:field> + </bcf:multiscriptfields> + <bcf:constraints> + <bcf:entrytype>article</bcf:entrytype> + <bcf:entrytype>book</bcf:entrytype> + <bcf:entrytype>inbook</bcf:entrytype> + <bcf:entrytype>bookinbook</bcf:entrytype> + <bcf:entrytype>suppbook</bcf:entrytype> + <bcf:entrytype>booklet</bcf:entrytype> + <bcf:entrytype>collection</bcf:entrytype> + <bcf:entrytype>incollection</bcf:entrytype> + <bcf:entrytype>suppcollection</bcf:entrytype> + <bcf:entrytype>manual</bcf:entrytype> + <bcf:entrytype>misc</bcf:entrytype> + <bcf:entrytype>mvbook</bcf:entrytype> + <bcf:entrytype>mvcollection</bcf:entrytype> + <bcf:entrytype>online</bcf:entrytype> + <bcf:entrytype>patent</bcf:entrytype> + <bcf:entrytype>periodical</bcf:entrytype> + <bcf:entrytype>suppperiodical</bcf:entrytype> + <bcf:entrytype>proceedings</bcf:entrytype> + <bcf:entrytype>inproceedings</bcf:entrytype> + <bcf:entrytype>reference</bcf:entrytype> + <bcf:entrytype>inreference</bcf:entrytype> + <bcf:entrytype>report</bcf:entrytype> + <bcf:entrytype>set</bcf:entrytype> + <bcf:entrytype>thesis</bcf:entrytype> + <bcf:entrytype>unpublished</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:fieldxor> + <bcf:field>date</bcf:field> + <bcf:field>year</bcf:field> + </bcf:fieldxor> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>set</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>entryset</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>article</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>author</bcf:field> + <bcf:field>journaltitle</bcf:field> + <bcf:field>title</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>book</bcf:entrytype> + <bcf:entrytype>mvbook</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>author</bcf:field> + <bcf:field>title</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>inbook</bcf:entrytype> + <bcf:entrytype>bookinbook</bcf:entrytype> + <bcf:entrytype>suppbook</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>author</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>booktitle</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>booklet</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:fieldor> + <bcf:field>author</bcf:field> + <bcf:field>editor</bcf:field> + </bcf:fieldor> + <bcf:field>title</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>collection</bcf:entrytype> + <bcf:entrytype>reference</bcf:entrytype> + <bcf:entrytype>mvcollection</bcf:entrytype> + <bcf:entrytype>mvreference</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>editor</bcf:field> + <bcf:field>title</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>incollection</bcf:entrytype> + <bcf:entrytype>suppcollection</bcf:entrytype> + <bcf:entrytype>inreference</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>author</bcf:field> + <bcf:field>editor</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>booktitle</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>dataset</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>title</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>manual</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>title</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>misc</bcf:entrytype> + <bcf:entrytype>software</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>title</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>online</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>title</bcf:field> + <bcf:fieldor> + <bcf:field>url</bcf:field> + <bcf:field>doi</bcf:field> + <bcf:field>eprint</bcf:field> + </bcf:fieldor> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>patent</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>author</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>number</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>periodical</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>editor</bcf:field> + <bcf:field>title</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>proceedings</bcf:entrytype> + <bcf:entrytype>mvproceedings</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>title</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>inproceedings</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>author</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>booktitle</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>report</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>author</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>type</bcf:field> + <bcf:field>institution</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>thesis</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>author</bcf:field> + <bcf:field>title</bcf:field> + <bcf:field>type</bcf:field> + <bcf:field>institution</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:entrytype>unpublished</bcf:entrytype> + <bcf:constraint type="mandatory"> + <bcf:field>author</bcf:field> + <bcf:field>title</bcf:field> + </bcf:constraint> + </bcf:constraints> + <bcf:constraints> + <bcf:constraint type="data" datatype="isbn"> + <bcf:field>isbn</bcf:field> + </bcf:constraint> + <bcf:constraint type="data" datatype="issn"> + <bcf:field>issn</bcf:field> + </bcf:constraint> + <bcf:constraint type="data" datatype="ismn"> + <bcf:field>ismn</bcf:field> + </bcf:constraint> + <bcf:constraint type="data" datatype="pattern" pattern="(?:sf|sm|sn|pf|pm|pn|pp)"> + <bcf:field>gender</bcf:field> + </bcf:constraint> + </bcf:constraints> + </bcf:datamodel> + <!-- CITATION DATA --> + <!-- SECTION 0 --> + <bcf:bibdata section="0"> + </bcf:bibdata> + <bcf:section number="0"> + </bcf:section> + <!-- SORTING TEMPLATES --> + <bcf:sortingtemplate name="nty"> + <bcf:sort order="1"> + <bcf:sortitem order="1">presort</bcf:sortitem> + </bcf:sort> + <bcf:sort order="2" final="1"> + <bcf:sortitem order="1">sortkey</bcf:sortitem> + </bcf:sort> + <bcf:sort order="3"> + <bcf:sortitem order="1">sortname</bcf:sortitem> + <bcf:sortitem order="2">author</bcf:sortitem> + <bcf:sortitem order="3">editor</bcf:sortitem> + <bcf:sortitem order="4">translator</bcf:sortitem> + <bcf:sortitem order="5">sorttitle</bcf:sortitem> + <bcf:sortitem order="6">title</bcf:sortitem> + </bcf:sort> + <bcf:sort order="4"> + <bcf:sortitem order="1">sorttitle</bcf:sortitem> + <bcf:sortitem order="2">title</bcf:sortitem> + </bcf:sort> + <bcf:sort order="5"> + <bcf:sortitem order="1">sortyear</bcf:sortitem> + <bcf:sortitem order="2">year</bcf:sortitem> + </bcf:sort> + <bcf:sort order="6"> + <bcf:sortitem order="1">volume</bcf:sortitem> + <bcf:sortitem literal="1" order="2">0</bcf:sortitem> + </bcf:sort> + </bcf:sortingtemplate> + <!-- DATALISTS --> +</bcf:controlfile> diff --git a/6th-Semester-Spring-2024/EnI/Assignments/LinkedIn-Summary/LinkedIn-Summary.blg b/6th-Semester-Spring-2024/EnI/Assignments/LinkedIn-Summary/LinkedIn-Summary.blg new file mode 100644 index 0000000..3ce8d48 --- /dev/null +++ b/6th-Semester-Spring-2024/EnI/Assignments/LinkedIn-Summary/LinkedIn-Summary.blg @@ -0,0 +1,4 @@ +[0] Config.pm:306> INFO - This is Biber 2.18 +[0] Config.pm:309> INFO - Logfile is 'LinkedIn-Summary.blg' +[74] biber:340> INFO - === Sun Jan 21, 2024, 15:04:02 +[93] Biber.pm:418> INFO - Reading 'LinkedIn-Summary.bcf' diff --git a/6th-Semester-Spring-2024/EnI/Assignments/LinkedIn-Summary/LinkedIn-Summary.fdb_latexmk b/6th-Semester-Spring-2024/EnI/Assignments/LinkedIn-Summary/LinkedIn-Summary.fdb_latexmk new file mode 100644 index 0000000..415214e --- /dev/null +++ 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<file>LinkedIn-Summary.bbl</file> + </output> + <provides type="dynamic"> + <file>LinkedIn-Summary.bbl</file> + </provides> + <requires type="dynamic"> + <file>LinkedIn-Summary.bcf</file> + </requires> + </external> +</requests> diff --git a/6th-Semester-Spring-2024/EnI/Assignments/LinkedIn-Summary/LinkedIn-Summary.synctex.gz b/6th-Semester-Spring-2024/EnI/Assignments/LinkedIn-Summary/LinkedIn-Summary.synctex.gz new file mode 100644 index 0000000..8fe4584 Binary files /dev/null and b/6th-Semester-Spring-2024/EnI/Assignments/LinkedIn-Summary/LinkedIn-Summary.synctex.gz differ diff --git a/6th-Semester-Spring-2024/EnI/Assignments/LinkedIn-Summary/LinkedIn-Summary.tex b/6th-Semester-Spring-2024/EnI/Assignments/LinkedIn-Summary/LinkedIn-Summary.tex new file mode 100644 index 0000000..37f9c96 --- /dev/null +++ b/6th-Semester-Spring-2024/EnI/Assignments/LinkedIn-Summary/LinkedIn-Summary.tex @@ -0,0 +1,19 @@ +\documentclass{mla} + +\title{LinkedIn Profile Summary} +\author{Aidan Sharpe} +\professor{Prof. Payton} + +\begin{document} + +Aidan Sharpe takes the saying "Learn Something new Everyday" to the next level. He has been programming since he was in the fifth grade, and continues to learn and grow to this day. In high school, he lead the "Programming \& Electronics" committee on FIRST Robotics Competition team 1089, which inspired him to pursue Electrical and Computer Engineering (ECE) in college. + +Most ECEs have a preference for either electrical engineering or computer engineering, but Aidan loves both. At his internship at Inductotherm, he excelled at using both disciplines in a professional setting. He used his software engineering skills to automate internet of things configuration processes and his electronics skills to extend the functionality of a test fixture with a custom circuit board. + +In his free time, Aidan continues to learn. He completes personal electronics and software projects, and one of his hobbies is tinkering with his Linux configuration. Aidan has been a full-time Linux user for almost two years, and has no plans of switching back to Windows. He has mastered the terminal and uses it for everything from file management, to writing notes and code, to making to-do lists, and even, at one point, to play music with Spotify. + +Aidan is also pursuing two certificates of undergraduate study (CUGS): Cyber security, and cyber security engineering. While taking courses towards these certificates, Aidan has reaffirmed that using Linux was a great choice towards personal security. + +Another one of Aidan's passions is teaching others. While some tutor to earn money, Aidan hosts workshops for other Electrical and Computer Engineers to satisfy his desire to teach. As an Eagle Scout and a Sailing Coach, Aidan learned how to effectively organize, communicate with, and teach others. He has absolutely no fear of public speaking or meeting and getting to know new people. + +\end{document} diff --git a/6th-Semester-Spring-2024/EnI/Group Work/fleshing_out_ideas.wiki b/6th-Semester-Spring-2024/EnI/Group Work/fleshing_out_ideas.wiki new file mode 100644 index 0000000..ef2585f --- /dev/null +++ b/6th-Semester-Spring-2024/EnI/Group Work/fleshing_out_ideas.wiki @@ -0,0 +1,92 @@ += Brainstorming = +1. Fitness Tracker + a) Social fitness tracker that sorts people into groups. + b) *TARGET MARKET:* + i) Would be people that like "gamified" apps like *Duolingo*. TikTok and Instagram seem to be solid marketing bases. +2. Online bullet journal / bullet journal app + a) Setup preset items (bullet points, tasks, checkboxes, progress bars) with custom or pre-made drawings + b) Easy to edit, insert + c) Minimal interface (mobile-friendly, tablet-friendly, keyboard-friendly) + d) Vim-like keybindings? + e) *TARGET MARKET:* + i) Current tablet and laptop note takers +3. Fitness to-do list + a) Notifications/reminders for water and supplements. + b) *TARGET MARKET* people who are looking for a way to kickstart an active lifestyle + i) Habits take time and practice to build +4. Emergency prep kit + a) Batteries, first-aid, flashlights, small handtools + b) Easy to keep in a glove box or night stand drawer + c) Discuss hard case vs. soft case + d) *TARGET MARKET:* + i) Car and truck owners + ii) Mothers +5. 3D-printed play therapy items + a) Explore TPU and other flexible materials + b) Motor skill improvement + c) *TARGET MARKET:* + i) people with reduced motor skills and dexterity +6. Reward system for journaling with 3D-printed prizes + a) What to reward? + b) What service is being paid for? + i) Self-help rewards service? + ii) Why not just buy the reward items outright? +7. Brainstorming with AI assessments + a) Use current events to tie ideas back to real-world + b) Come up with related ideas + c) *TARGET MARKET:* + i) Students with group projects + ii) Entrepreneurs +8. 3D printed housing + a) Would require consulting civil engineer to evaluate viability + b) Has been successfully implemented + c) What new approach would we take? + d) *TARGET MARKET:* + i) Affordable, mass produced housing +9. Phone button + a) Tap for loud noise + b) *TARGET MARKET:* + i) Elderly + ii) Young people +10. Panic/anxiety attack guide + a) Personable + b) AI therapist + c) App/hotline + d) *TARGET MARKET:* + i) 911 dispatchers + ii) People prone to anxiety or panic attacks +11. Self-health rating app + a) Regular check-up notifications + b) Algorithm-generated daily score + c) Doesn't need an internet connection + d) Keyword detection + i) Forward to 911 or a specialized hotline +12. Community-driven turbo tax alternative + a) Tax laws are complex + b) TurboTax has a significant market share + c) FOSS solutions exist but are not nearly as extensive as the proprietary competition + d) Many FOSS solutions only support common federal tax forms + e) *TARGET MARKET:* + a) US taxpayers currently using software similar to TurboTax + b) Especially those that do not qualify for the IRS FreeFile program +13. Social engagement for the elderly +14. Electronic donation system + a) Potentially partner with Lions Club similar to their glasses donation program + b) Reduce electronic waste + c) Encourages repair over disposal mindset + d) *TARGET MARKET:* + i) Receive donations from people with older models of phones, tablets, computers + ii) Encourage donations to underprivileged communities +15. Remote-controlled pet ball + a) Definitely possible with the team's skill-set + b) Would likely be quite fun to make + c) *TARGET MARKET:* + i) Pet owners + ii) Potentially could be a fun children's toy as well +16. Fridge inventory manager + a) Add items to keep track of + b) Increment and decrement food items in fridge + c) Help roomates know what needs to be restocked and what doesn't + d) *TARGET MARKET:* + i) College roomates with a fridge/pantry + ii) Young families diff --git a/6th-Semester-Spring-2024/EnI/Group Work/problem-list.wiki b/6th-Semester-Spring-2024/EnI/Group Work/problem-list.wiki new file mode 100644 index 0000000..c55be0f --- /dev/null +++ b/6th-Semester-Spring-2024/EnI/Group Work/problem-list.wiki @@ -0,0 +1,13 @@ += Sustainable Goals = +1. 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Quality Education + a) Slow note taking + b) diff --git a/6th-Semester-Spring-2024/EnI/Notes/EnI-notes.aux b/6th-Semester-Spring-2024/EnI/Notes/EnI-notes.aux new file mode 100644 index 0000000..36aa35c --- /dev/null +++ b/6th-Semester-Spring-2024/EnI/Notes/EnI-notes.aux @@ -0,0 +1,40 @@ +\relax +\providecommand{\transparent@use}[1]{} +\providecommand\hyper@newdestlabel[2]{} +\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} +\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined +\global\let\oldnewlabel\newlabel +\gdef\newlabel#1#2{\newlabelxx{#1}#2} +\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} +\AtEndDocument{\ifx\hyper@anchor\@undefined +\let\newlabel\oldnewlabel +\fi} +\fi} +\global\let\hyper@last\relax +\gdef\HyperFirstAtBeginDocument#1{#1} +\providecommand\HyField@AuxAddToFields[1]{} +\providecommand\HyField@AuxAddToCoFields[2]{} +\providecommand\BKM@entry[2]{} +\providecommand \oddpage@label [2]{} 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b/6th-Semester-Spring-2024/EnI/Notes/EnI-notes.pdf new file mode 100644 index 0000000..c22818f Binary files /dev/null and b/6th-Semester-Spring-2024/EnI/Notes/EnI-notes.pdf differ diff --git a/6th-Semester-Spring-2024/EnI/Notes/EnI-notes.synctex.gz b/6th-Semester-Spring-2024/EnI/Notes/EnI-notes.synctex.gz new file mode 100644 index 0000000..7669ed4 Binary files /dev/null and b/6th-Semester-Spring-2024/EnI/Notes/EnI-notes.synctex.gz differ diff --git a/6th-Semester-Spring-2024/EnI/Notes/EnI-notes.tex b/6th-Semester-Spring-2024/EnI/Notes/EnI-notes.tex new file mode 100644 index 0000000..8717acc --- /dev/null +++ b/6th-Semester-Spring-2024/EnI/Notes/EnI-notes.tex @@ -0,0 +1,94 @@ +\documentclass{report} + +\input{preamble} +\input{macros} +\input{letterfonts} + +\title{\Huge{Entrepreneurship and Innovation}} +\author{\huge{Aidan Sharpe}} +\date{} + +\begin{document} + +\maketitle +\newpage% or \cleardoublepage +% \pdfbookmark[<level>]{<title>}{<dest>} +\pdfbookmark[section]{\contentsname}{toc} +\tableofcontents +\pagebreak + +\chapter{} +\dfn{Entrepreneurship} +{ + According to Steve Blanc, \emph{Entrepreneurship} is the search for a sustainable and repeatable process to validate a business idea. +} + +The difference between a startup and a business is that a startup is a hypothesis test for a process, while a business is the tested idea. + +\dfn{Intrapreneurship} +{ + The act of behaving like an entrepreneur while working within a large organization. +} + +\dfn{Bootstrapping} +{ + Being able to create a startup with minimal budget and without external funds. +} + +\dfn{Pitch Deck} +{ + A marketing presentation used to gain investors and funding. +} + +The design thinking process: +\begin{enumerate} + \item \textbf{Empathize}: understand what the customer \emph{wants} and \emph{needs} + \item \textbf{Define} + \item \textbf{Ideate} + \item \textbf{Prototype} + \item \textbf{Test} +\end{enumerate} + +\dfn{Growth Mindset} +{ + +} + +\dfn{Ideation} +{ + The act of generating, developing, and communicating new ideas. +} + +\chapter{} + +\section{Business Model} +\dfn{Business Model} +{ + Describes the rationale of how a new venture delivers and captures value +} +\noindent +A business model canvas has nine segments in four core areas. +\begin{enumerate} + \item \textbf{Offering}: Value generated and reaching customer base + \item \textbf{Customer}: Customers are + \item \textbf{Infrastructure}: includes all necessary resources to fulfill customer value proposition + \item \textbf{Financial Viability}: defines costs and revenue streams +\end{enumerate} + +\dfn{Customer Value Proposition (CVP)} +{ + Better value than competition. Measurable in monetary terms. Must be sustainable for long-term operation. +} + +\subsection{Business Model Canvas} +\begin{enumerate} + \item \textbf{Customer Value Proposition}: properly addresses the need + \item \textbf{Customer Segments}: + \item \textbf{Customer Relationships}: People want to know that you care. How to get, keep, and grow a customer base. +\end{enumerate} +\dfn{Minimum Value Proposition} +{ + Meets needs and requirements of the CVP while mitigating risk +} + +\end{document} diff --git a/6th-Semester-Spring-2024/EnI/Notes/EnI-notes.toc b/6th-Semester-Spring-2024/EnI/Notes/EnI-notes.toc new file mode 100644 index 0000000..09a2554 --- /dev/null +++ b/6th-Semester-Spring-2024/EnI/Notes/EnI-notes.toc @@ -0,0 +1,5 @@ +\contentsline {chapter}{\numberline {1}}{2}{chapter.1}% +\contentsline {chapter}{\numberline {2}}{3}{chapter.2}% +\contentsline {section}{\numberline {2.1}Business Model}{3}{section.2.1}% +\contentsline {subsection}{\numberline {2.1.1}Business Model Canvas}{3}{subsection.2.1.1}% +\contentsfinish diff --git a/6th-Semester-Spring-2024/EnI/Notes/letterfonts.tex b/6th-Semester-Spring-2024/EnI/Notes/letterfonts.tex new file mode 100644 index 0000000..e28675f --- /dev/null +++ b/6th-Semester-Spring-2024/EnI/Notes/letterfonts.tex @@ -0,0 +1,178 @@ +% Things Lie +\newcommand{\kb}{\mathfrak b} +\newcommand{\kg}{\mathfrak g} +\newcommand{\kh}{\mathfrak h} +\newcommand{\kn}{\mathfrak n} +\newcommand{\ku}{\mathfrak u} +\newcommand{\kz}{\mathfrak z} +\DeclareMathOperator{\Ext}{Ext} % Ext functor +\DeclareMathOperator{\Tor}{Tor} % Tor functor +\newcommand{\gl}{\opname{\mathfrak{gl}}} % frak gl group +\renewcommand{\sl}{\opname{\mathfrak{sl}}} % frak sl group chktex 6 + +% More script letters etc. +\newcommand{\SA}{\mathcal A} +\newcommand{\SB}{\mathcal B} +\newcommand{\SC}{\mathcal C} +\newcommand{\SF}{\mathcal F} +\newcommand{\SG}{\mathcal G} +\newcommand{\SH}{\mathcal H} +\newcommand{\OO}{\mathcal O} + +\newcommand{\SCA}{\mathscr A} +\newcommand{\SCB}{\mathscr B} +\newcommand{\SCC}{\mathscr C} +\newcommand{\SCD}{\mathscr D} +\newcommand{\SCE}{\mathscr E} +\newcommand{\SCF}{\mathscr F} +\newcommand{\SCG}{\mathscr G} +\newcommand{\SCH}{\mathscr H} + +% Mathfrak primes +\newcommand{\km}{\mathfrak m} +\newcommand{\kp}{\mathfrak p} +\newcommand{\kq}{\mathfrak q} + +% number sets +\newcommand{\RR}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{R}}{\mathbb{R}^{#1}}}} +\newcommand{\NN}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{N}}{\mathbb{N}^{#1}}}} +\newcommand{\ZZ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Z}}{\mathbb{Z}^{#1}}}} +\newcommand{\QQ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Q}}{\mathbb{Q}^{#1}}}} +\newcommand{\CC}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{C}}{\mathbb{C}^{#1}}}} +\newcommand{\PP}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{P}}{\mathbb{P}^{#1}}}} +\newcommand{\HH}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{H}}{\mathbb{H}^{#1}}}} +\newcommand{\FF}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{F}}{\mathbb{F}^{#1}}}} +% expected value +\newcommand{\EE}{\ensuremath{\mathbb{E}}} +\newcommand{\charin}{\text{ char }} +\DeclareMathOperator{\sign}{sign} +\DeclareMathOperator{\Aut}{Aut} +\DeclareMathOperator{\Inn}{Inn} +\DeclareMathOperator{\Syl}{Syl} +\DeclareMathOperator{\Gal}{Gal} +\DeclareMathOperator{\GL}{GL} % General linear group +\DeclareMathOperator{\SL}{SL} % Special linear group + +%--------------------------------------- +% BlackBoard Math Fonts :- +%--------------------------------------- + +%Captital Letters +\newcommand{\bbA}{\mathbb{A}} \newcommand{\bbB}{\mathbb{B}} +\newcommand{\bbC}{\mathbb{C}} \newcommand{\bbD}{\mathbb{D}} +\newcommand{\bbE}{\mathbb{E}} \newcommand{\bbF}{\mathbb{F}} +\newcommand{\bbG}{\mathbb{G}} \newcommand{\bbH}{\mathbb{H}} +\newcommand{\bbI}{\mathbb{I}} \newcommand{\bbJ}{\mathbb{J}} +\newcommand{\bbK}{\mathbb{K}} \newcommand{\bbL}{\mathbb{L}} +\newcommand{\bbM}{\mathbb{M}} \newcommand{\bbN}{\mathbb{N}} +\newcommand{\bbO}{\mathbb{O}} \newcommand{\bbP}{\mathbb{P}} +\newcommand{\bbQ}{\mathbb{Q}} \newcommand{\bbR}{\mathbb{R}} +\newcommand{\bbS}{\mathbb{S}} \newcommand{\bbT}{\mathbb{T}} +\newcommand{\bbU}{\mathbb{U}} \newcommand{\bbV}{\mathbb{V}} +\newcommand{\bbW}{\mathbb{W}} \newcommand{\bbX}{\mathbb{X}} +\newcommand{\bbY}{\mathbb{Y}} \newcommand{\bbZ}{\mathbb{Z}} + +%--------------------------------------- +% MathCal Fonts :- +%--------------------------------------- + +%Captital Letters +\newcommand{\mcA}{\mathcal{A}} \newcommand{\mcB}{\mathcal{B}} +\newcommand{\mcC}{\mathcal{C}} \newcommand{\mcD}{\mathcal{D}} +\newcommand{\mcE}{\mathcal{E}} \newcommand{\mcF}{\mathcal{F}} +\newcommand{\mcG}{\mathcal{G}} \newcommand{\mcH}{\mathcal{H}} +\newcommand{\mcI}{\mathcal{I}} \newcommand{\mcJ}{\mathcal{J}} +\newcommand{\mcK}{\mathcal{K}} \newcommand{\mcL}{\mathcal{L}} +\newcommand{\mcM}{\mathcal{M}} \newcommand{\mcN}{\mathcal{N}} +\newcommand{\mcO}{\mathcal{O}} \newcommand{\mcP}{\mathcal{P}} +\newcommand{\mcQ}{\mathcal{Q}} \newcommand{\mcR}{\mathcal{R}} +\newcommand{\mcS}{\mathcal{S}} \newcommand{\mcT}{\mathcal{T}} +\newcommand{\mcU}{\mathcal{U}} \newcommand{\mcV}{\mathcal{V}} +\newcommand{\mcW}{\mathcal{W}} \newcommand{\mcX}{\mathcal{X}} +\newcommand{\mcY}{\mathcal{Y}} \newcommand{\mcZ}{\mathcal{Z}} + + +%--------------------------------------- +% Bold Math Fonts :- +%--------------------------------------- + +%Captital Letters +\newcommand{\bmA}{\boldsymbol{A}} \newcommand{\bmB}{\boldsymbol{B}} +\newcommand{\bmC}{\boldsymbol{C}} \newcommand{\bmD}{\boldsymbol{D}} +\newcommand{\bmE}{\boldsymbol{E}} \newcommand{\bmF}{\boldsymbol{F}} +\newcommand{\bmG}{\boldsymbol{G}} \newcommand{\bmH}{\boldsymbol{H}} +\newcommand{\bmI}{\boldsymbol{I}} \newcommand{\bmJ}{\boldsymbol{J}} +\newcommand{\bmK}{\boldsymbol{K}} \newcommand{\bmL}{\boldsymbol{L}} +\newcommand{\bmM}{\boldsymbol{M}} \newcommand{\bmN}{\boldsymbol{N}} +\newcommand{\bmO}{\boldsymbol{O}} \newcommand{\bmP}{\boldsymbol{P}} +\newcommand{\bmQ}{\boldsymbol{Q}} \newcommand{\bmR}{\boldsymbol{R}} +\newcommand{\bmS}{\boldsymbol{S}} \newcommand{\bmT}{\boldsymbol{T}} +\newcommand{\bmU}{\boldsymbol{U}} \newcommand{\bmV}{\boldsymbol{V}} +\newcommand{\bmW}{\boldsymbol{W}} \newcommand{\bmX}{\boldsymbol{X}} +\newcommand{\bmY}{\boldsymbol{Y}} \newcommand{\bmZ}{\boldsymbol{Z}} +%Small Letters +\newcommand{\bma}{\boldsymbol{a}} \newcommand{\bmb}{\boldsymbol{b}} +\newcommand{\bmc}{\boldsymbol{c}} \newcommand{\bmd}{\boldsymbol{d}} +\newcommand{\bme}{\boldsymbol{e}} \newcommand{\bmf}{\boldsymbol{f}} +\newcommand{\bmg}{\boldsymbol{g}} \newcommand{\bmh}{\boldsymbol{h}} +\newcommand{\bmi}{\boldsymbol{i}} \newcommand{\bmj}{\boldsymbol{j}} +\newcommand{\bmk}{\boldsymbol{k}} \newcommand{\bml}{\boldsymbol{l}} +\newcommand{\bmm}{\boldsymbol{m}} \newcommand{\bmn}{\boldsymbol{n}} +\newcommand{\bmo}{\boldsymbol{o}} \newcommand{\bmp}{\boldsymbol{p}} +\newcommand{\bmq}{\boldsymbol{q}} \newcommand{\bmr}{\boldsymbol{r}} +\newcommand{\bms}{\boldsymbol{s}} \newcommand{\bmt}{\boldsymbol{t}} +\newcommand{\bmu}{\boldsymbol{u}} \newcommand{\bmv}{\boldsymbol{v}} +\newcommand{\bmw}{\boldsymbol{w}} \newcommand{\bmx}{\boldsymbol{x}} +\newcommand{\bmy}{\boldsymbol{y}} \newcommand{\bmz}{\boldsymbol{z}} + +%--------------------------------------- +% Scr Math Fonts :- +%--------------------------------------- + +\newcommand{\sA}{{\mathscr{A}}} \newcommand{\sB}{{\mathscr{B}}} +\newcommand{\sC}{{\mathscr{C}}} \newcommand{\sD}{{\mathscr{D}}} +\newcommand{\sE}{{\mathscr{E}}} \newcommand{\sF}{{\mathscr{F}}} +\newcommand{\sG}{{\mathscr{G}}} \newcommand{\sH}{{\mathscr{H}}} +\newcommand{\sI}{{\mathscr{I}}} \newcommand{\sJ}{{\mathscr{J}}} +\newcommand{\sK}{{\mathscr{K}}} \newcommand{\sL}{{\mathscr{L}}} +\newcommand{\sM}{{\mathscr{M}}} \newcommand{\sN}{{\mathscr{N}}} +\newcommand{\sO}{{\mathscr{O}}} \newcommand{\sP}{{\mathscr{P}}} +\newcommand{\sQ}{{\mathscr{Q}}} \newcommand{\sR}{{\mathscr{R}}} +\newcommand{\sS}{{\mathscr{S}}} \newcommand{\sT}{{\mathscr{T}}} +\newcommand{\sU}{{\mathscr{U}}} \newcommand{\sV}{{\mathscr{V}}} +\newcommand{\sW}{{\mathscr{W}}} \newcommand{\sX}{{\mathscr{X}}} +\newcommand{\sY}{{\mathscr{Y}}} \newcommand{\sZ}{{\mathscr{Z}}} + + +%--------------------------------------- +% Math Fraktur Font +%--------------------------------------- + +%Captital Letters +\newcommand{\mfA}{\mathfrak{A}} \newcommand{\mfB}{\mathfrak{B}} +\newcommand{\mfC}{\mathfrak{C}} \newcommand{\mfD}{\mathfrak{D}} +\newcommand{\mfE}{\mathfrak{E}} \newcommand{\mfF}{\mathfrak{F}} +\newcommand{\mfG}{\mathfrak{G}} \newcommand{\mfH}{\mathfrak{H}} +\newcommand{\mfI}{\mathfrak{I}} \newcommand{\mfJ}{\mathfrak{J}} +\newcommand{\mfK}{\mathfrak{K}} \newcommand{\mfL}{\mathfrak{L}} +\newcommand{\mfM}{\mathfrak{M}} \newcommand{\mfN}{\mathfrak{N}} +\newcommand{\mfO}{\mathfrak{O}} \newcommand{\mfP}{\mathfrak{P}} +\newcommand{\mfQ}{\mathfrak{Q}} \newcommand{\mfR}{\mathfrak{R}} +\newcommand{\mfS}{\mathfrak{S}} \newcommand{\mfT}{\mathfrak{T}} +\newcommand{\mfU}{\mathfrak{U}} \newcommand{\mfV}{\mathfrak{V}} +\newcommand{\mfW}{\mathfrak{W}} \newcommand{\mfX}{\mathfrak{X}} +\newcommand{\mfY}{\mathfrak{Y}} \newcommand{\mfZ}{\mathfrak{Z}} +%Small Letters +\newcommand{\mfa}{\mathfrak{a}} \newcommand{\mfb}{\mathfrak{b}} +\newcommand{\mfc}{\mathfrak{c}} \newcommand{\mfd}{\mathfrak{d}} +\newcommand{\mfe}{\mathfrak{e}} \newcommand{\mff}{\mathfrak{f}} +\newcommand{\mfg}{\mathfrak{g}} \newcommand{\mfh}{\mathfrak{h}} +\newcommand{\mfi}{\mathfrak{i}} \newcommand{\mfj}{\mathfrak{j}} +\newcommand{\mfk}{\mathfrak{k}} \newcommand{\mfl}{\mathfrak{l}} +\newcommand{\mfm}{\mathfrak{m}} \newcommand{\mfn}{\mathfrak{n}} +\newcommand{\mfo}{\mathfrak{o}} \newcommand{\mfp}{\mathfrak{p}} +\newcommand{\mfq}{\mathfrak{q}} \newcommand{\mfr}{\mathfrak{r}} +\newcommand{\mfs}{\mathfrak{s}} \newcommand{\mft}{\mathfrak{t}} +\newcommand{\mfu}{\mathfrak{u}} \newcommand{\mfv}{\mathfrak{v}} +\newcommand{\mfw}{\mathfrak{w}} \newcommand{\mfx}{\mathfrak{x}} +\newcommand{\mfy}{\mathfrak{y}} \newcommand{\mfz}{\mathfrak{z}} diff --git a/6th-Semester-Spring-2024/EnI/Notes/macros.tex b/6th-Semester-Spring-2024/EnI/Notes/macros.tex new file mode 100644 index 0000000..8bbdb96 --- /dev/null +++ b/6th-Semester-Spring-2024/EnI/Notes/macros.tex @@ -0,0 +1,88 @@ +%From M275 "Topology" at SJSU +\newcommand{\id}{\mathrm{id}} +\newcommand{\taking}[1]{\xrightarrow{#1}} +\newcommand{\inv}{^{-1}} + +%From M170 "Introduction to Graph Theory" at SJSU +\DeclareMathOperator{\diam}{diam} +\DeclareMathOperator{\ord}{ord} +\newcommand{\defeq}{\overset{\mathrm{def}}{=}} + +%From the USAMO .tex files +\newcommand{\ts}{\textsuperscript} +\newcommand{\dg}{^\circ} +\newcommand{\ii}{\item} + +% % From Math 55 and Math 145 at Harvard +% \newenvironment{subproof}[1][Proof]{% +% \begin{proof}[#1] \renewcommand{\qedsymbol}{$\blacksquare$}}% +% {\end{proof}} + +\newcommand{\liff}{\leftrightarrow} +\newcommand{\lthen}{\rightarrow} +\newcommand{\opname}{\operatorname} +\newcommand{\surjto}{\twoheadrightarrow} +\newcommand{\injto}{\hookrightarrow} +\newcommand{\On}{\mathrm{On}} % ordinals +\DeclareMathOperator{\img}{im} % Image +\DeclareMathOperator{\Img}{Im} % Image +\DeclareMathOperator{\coker}{coker} % Cokernel +\DeclareMathOperator{\Coker}{Coker} % Cokernel +\DeclareMathOperator{\Ker}{Ker} % Kernel +\DeclareMathOperator{\rank}{rank} +\DeclareMathOperator{\Spec}{Spec} % spectrum +\DeclareMathOperator{\Tr}{Tr} % trace +\DeclareMathOperator{\pr}{pr} % projection +\DeclareMathOperator{\ext}{ext} % extension +\DeclareMathOperator{\pred}{pred} % predecessor +\DeclareMathOperator{\dom}{dom} % domain +\DeclareMathOperator{\ran}{ran} % range +\DeclareMathOperator{\Hom}{Hom} % homomorphism +\DeclareMathOperator{\Mor}{Mor} % morphisms +\DeclareMathOperator{\End}{End} % endomorphism + +\newcommand{\eps}{\epsilon} +\newcommand{\veps}{\varepsilon} +\newcommand{\ol}{\overline} +\newcommand{\ul}{\underline} +\newcommand{\wt}{\widetilde} +\newcommand{\wh}{\widehat} +\newcommand{\vocab}[1]{\textbf{\color{blue} #1}} +\providecommand{\half}{\frac{1}{2}} +\newcommand{\dang}{\measuredangle} %% Directed angle +\newcommand{\ray}[1]{\overrightarrow{#1}} +\newcommand{\seg}[1]{\overline{#1}} +\newcommand{\arc}[1]{\wideparen{#1}} +\DeclareMathOperator{\cis}{cis} +\DeclareMathOperator*{\lcm}{lcm} +\DeclareMathOperator*{\argmin}{arg min} +\DeclareMathOperator*{\argmax}{arg max} +\newcommand{\cycsum}{\sum_{\mathrm{cyc}}} +\newcommand{\symsum}{\sum_{\mathrm{sym}}} +\newcommand{\cycprod}{\prod_{\mathrm{cyc}}} +\newcommand{\symprod}{\prod_{\mathrm{sym}}} +\newcommand{\Qed}{\begin{flushright}\qed\end{flushright}} +\newcommand{\parinn}{\setlength{\parindent}{1cm}} +\newcommand{\parinf}{\setlength{\parindent}{0cm}} +% \newcommand{\norm}{\|\cdot\|} +\newcommand{\inorm}{\norm_{\infty}} +\newcommand{\opensets}{\{V_{\alpha}\}_{\alpha\in I}} +\newcommand{\oset}{V_{\alpha}} +\newcommand{\opset}[1]{V_{\alpha_{#1}}} +\newcommand{\lub}{\text{lub}} +\newcommand{\del}[2]{\frac{\partial #1}{\partial #2}} +\newcommand{\Del}[3]{\frac{\partial^{#1} #2}{\partial^{#1} #3}} +\newcommand{\deld}[2]{\dfrac{\partial #1}{\partial #2}} +\newcommand{\Deld}[3]{\dfrac{\partial^{#1} #2}{\partial^{#1} #3}} +\newcommand{\lm}{\lambda} +\newcommand{\uin}{\mathbin{\rotatebox[origin=c]{90}{$\in$}}} +\newcommand{\usubset}{\mathbin{\rotatebox[origin=c]{90}{$\subset$}}} +\newcommand{\lt}{\left} +\newcommand{\rt}{\right} +\newcommand{\bs}[1]{\boldsymbol{#1}} +\newcommand{\exs}{\exists} +\newcommand{\st}{\strut} +\newcommand{\dps}[1]{\displaystyle{#1}} + +\newcommand{\sol}{\setlength{\parindent}{0cm}\textbf{\textit{Solution:}}\setlength{\parindent}{1cm} } +\newcommand{\solve}[1]{\setlength{\parindent}{0cm}\textbf{\textit{Solution: }}\setlength{\parindent}{1cm}#1 \Qed} diff --git a/6th-Semester-Spring-2024/EnI/Notes/preamble.tex b/6th-Semester-Spring-2024/EnI/Notes/preamble.tex new file mode 100644 index 0000000..af7d68e --- /dev/null +++ b/6th-Semester-Spring-2024/EnI/Notes/preamble.tex @@ -0,0 +1,779 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PACKAGE IMPORTS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\usepackage[tmargin=2cm,rmargin=1in,lmargin=1in,margin=0.85in,bmargin=2cm,footskip=.2in]{geometry} +\usepackage{amsmath,amsfonts,amsthm,amssymb,mathtools} +\usepackage{listings} +\usepackage[varbb]{newpxmath} +\usepackage{xfrac} +\usepackage[makeroom]{cancel} +\usepackage{mathtools} +\usepackage{bookmark} +\usepackage{enumitem} +\usepackage{hyperref,theoremref} +\hypersetup{ + pdftitle={Assignment}, + colorlinks=true, linkcolor=doc!90, + bookmarksnumbered=true, + bookmarksopen=true +} +\usepackage[most,many,breakable]{tcolorbox} +\usepackage{xcolor} +\usepackage{varwidth} +\usepackage{varwidth} +\usepackage{etoolbox} +%\usepackage{authblk} +\usepackage{nameref} +\usepackage{multicol,array} +\usepackage{tikz-cd} +\usepackage[ruled,vlined,linesnumbered]{algorithm2e} +\usepackage{comment} % enables the use of multi-line comments (\ifx \fi) +\usepackage{import} +\usepackage{xifthen} +\usepackage{pdfpages} +\usepackage{transparent} + +\newcommand\mycommfont[1]{\footnotesize\ttfamily\textcolor{blue}{#1}} +\SetCommentSty{mycommfont} +\newcommand{\incfig}[1]{% + \def\svgwidth{\columnwidth} + \import{./figures/}{#1.pdf_tex} +} + +\usepackage{tikzsymbols} +\renewcommand\qedsymbol{$\Laughey$} + + +%\usepackage{import} +%\usepackage{xifthen} +%\usepackage{pdfpages} +%\usepackage{transparent} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% SELF MADE COLORS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +\definecolor{myg}{RGB}{56, 140, 70} +\definecolor{myb}{RGB}{45, 111, 177} +\definecolor{myr}{RGB}{199, 68, 64} +\definecolor{mytheorembg}{HTML}{F2F2F9} +\definecolor{mytheoremfr}{HTML}{00007B} +\definecolor{mylenmabg}{HTML}{FFFAF8} +\definecolor{mylenmafr}{HTML}{983b0f} +\definecolor{mypropbg}{HTML}{f2fbfc} +\definecolor{mypropfr}{HTML}{191971} +\definecolor{myexamplebg}{HTML}{F2FBF8} +\definecolor{myexamplefr}{HTML}{88D6D1} +\definecolor{myexampleti}{HTML}{2A7F7F} +\definecolor{mydefinitbg}{HTML}{E5E5FF} +\definecolor{mydefinitfr}{HTML}{3F3FA3} +\definecolor{notesgreen}{RGB}{0,162,0} +\definecolor{myp}{RGB}{197, 92, 212} +\definecolor{mygr}{HTML}{2C3338} +\definecolor{myred}{RGB}{127,0,0} 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{2pt}{0pt}{mytheoremfr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mytheoremfr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mytheoremfr}, +} +{th} + + +\tcbuselibrary{theorems,skins,hooks} +\newtcolorbox{Theoremcon} +{% + enhanced + ,breakable + ,colback = mytheorembg + ,frame hidden + ,boxrule = 0sp + ,borderline west = {2pt}{0pt}{mytheoremfr} + ,sharp corners + ,description font = \mdseries + ,separator sign none +} + +%================================ +% Corollery +%================================ +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{Corollary}{Corollary} +{% + enhanced + ,breakable + ,colback = myp!10 + ,frame hidden + ,boxrule = 0sp + ,borderline west = {2pt}{0pt}{myp!85!black} + ,sharp corners + ,detach title + ,before upper = \tcbtitle\par\smallskip + ,coltitle = myp!85!black + ,fonttitle = \bfseries\sffamily + ,description font = \mdseries + ,separator sign none + ,segmentation style={solid, myp!85!black} +} +{th} +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=chapter]{corollary}{Corollary} +{% + enhanced + ,breakable + ,colback = myp!10 + ,frame hidden + ,boxrule = 0sp + ,borderline west = {2pt}{0pt}{myp!85!black} + ,sharp corners + ,detach title + ,before upper = \tcbtitle\par\smallskip + ,coltitle = myp!85!black + ,fonttitle = \bfseries\sffamily + ,description font = \mdseries + ,separator sign none + ,segmentation style={solid, myp!85!black} +} +{th} + + +%================================ +% LENMA +%================================ + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{Review}{Review} +{% + enhanced, + breakable, + colback = mylenmabg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{mylenmafr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mylenmafr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mylenmafr}, +} +{th} + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=chapter]{review}{Review} +{% + enhanced, + breakable, + colback = mylenmabg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{mylenmafr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mylenmafr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mylenmafr}, +} +{th} + + +%================================ +% METHOD +%================================ + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{Method}{Method} +{% + enhanced, + breakable, + colback = mypropbg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{mypropfr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mypropfr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mypropfr}, +} +{th} + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=chapter]{method}{Method} +{% + enhanced, + breakable, + colback = mypropbg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{mypropfr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mypropfr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mypropfr}, +} +{th} + + +%================================ +% CLAIM +%================================ + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{claim}{Claim} +{% + enhanced + ,breakable + ,colback = myg!10 + ,frame hidden + ,boxrule = 0sp + ,borderline west = {2pt}{0pt}{myg} + ,sharp corners + ,detach title + ,before upper = \tcbtitle\par\smallskip + ,coltitle = myg!85!black + ,fonttitle = \bfseries\sffamily + ,description font = \mdseries + ,separator sign none + ,segmentation style={solid, myg!85!black} +} +{th} + + + +%================================ +% Exercise +%================================ + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{Exercise}{Exercise} +{% + enhanced, + breakable, + colback = myexercisebg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{myexercisefg}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = myexercisefg, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, myexercisefg}, +} +{th} + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=chapter]{exercise}{Exercise} +{% + enhanced, + breakable, + colback = myexercisebg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{myexercisefg}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = myexercisefg, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, myexercisefg}, +} +{th} + +%================================ +% EXAMPLE BOX +%================================ + +\newtcbtheorem[number within=section]{Example}{Example} +{% + colback = myexamplebg + ,breakable + ,colframe = myexamplefr + ,coltitle = myexampleti + ,boxrule = 1pt + ,sharp corners + ,detach title + ,before upper=\tcbtitle\par\smallskip + ,fonttitle = \bfseries + ,description font = \mdseries + ,separator sign none + ,description delimiters parenthesis +} +{ex} + +\newtcbtheorem[number within=chapter]{example}{Example} +{% + colback = myexamplebg + ,breakable + ,colframe = myexamplefr + ,coltitle = myexampleti + ,boxrule = 1pt + ,sharp corners + ,detach title + ,before upper=\tcbtitle\par\smallskip + ,fonttitle = \bfseries + ,description font = \mdseries + ,separator sign none + ,description delimiters parenthesis +} +{ex} + +%================================ +% DEFINITION BOX +%================================ + +\newtcbtheorem[number within=section]{Definition}{Definition}{enhanced, + before skip=2mm,after skip=2mm, colback=red!5,colframe=red!80!black,boxrule=0.5mm, + attach boxed title to top left={xshift=1cm,yshift*=1mm-\tcboxedtitleheight}, varwidth boxed title*=-3cm, + boxed title style={frame code={ + \path[fill=tcbcolback] + ([yshift=-1mm,xshift=-1mm]frame.north west) + arc[start angle=0,end angle=180,radius=1mm] + ([yshift=-1mm,xshift=1mm]frame.north east) + arc[start angle=180,end angle=0,radius=1mm]; + \path[left color=tcbcolback!60!black,right color=tcbcolback!60!black, + middle color=tcbcolback!80!black] + ([xshift=-2mm]frame.north west) -- ([xshift=2mm]frame.north east) + [rounded corners=1mm]-- ([xshift=1mm,yshift=-1mm]frame.north east) + -- (frame.south east) -- (frame.south west) + -- ([xshift=-1mm,yshift=-1mm]frame.north west) + [sharp corners]-- cycle; + },interior engine=empty, + }, + fonttitle=\bfseries, + title={#2},#1}{def} +\newtcbtheorem[number within=chapter]{definition}{Definition}{enhanced, + before skip=2mm,after skip=2mm, colback=red!5,colframe=red!80!black,boxrule=0.5mm, + attach boxed title to top left={xshift=1cm,yshift*=1mm-\tcboxedtitleheight}, varwidth boxed title*=-3cm, + boxed title style={frame code={ + \path[fill=tcbcolback] + ([yshift=-1mm,xshift=-1mm]frame.north west) + arc[start angle=0,end angle=180,radius=1mm] + ([yshift=-1mm,xshift=1mm]frame.north east) + arc[start angle=180,end angle=0,radius=1mm]; + \path[left color=tcbcolback!60!black,right color=tcbcolback!60!black, + middle color=tcbcolback!80!black] + ([xshift=-2mm]frame.north west) -- ([xshift=2mm]frame.north east) + [rounded corners=1mm]-- ([xshift=1mm,yshift=-1mm]frame.north east) + -- (frame.south east) -- (frame.south west) + -- ([xshift=-1mm,yshift=-1mm]frame.north west) + [sharp corners]-- cycle; + },interior engine=empty, + }, + fonttitle=\bfseries, + title={#2},#1}{def} + + + +%================================ +% Solution BOX +%================================ + +\makeatletter +\newtcbtheorem{question}{Question}{enhanced, + breakable, + colback=white, + colframe=myb!80!black, + attach boxed title to top left={yshift*=-\tcboxedtitleheight}, + fonttitle=\bfseries, + title={#2}, + boxed title size=title, + boxed title style={% + sharp corners, + rounded corners=northwest, + colback=tcbcolframe, + boxrule=0pt, + }, + underlay boxed title={% + \path[fill=tcbcolframe] (title.south west)--(title.south east) + to[out=0, in=180] ([xshift=5mm]title.east)-- + (title.center-|frame.east) + [rounded corners=\kvtcb@arc] |- + (frame.north) -| cycle; + }, + #1 +}{def} +\makeatother + +%================================ +% SOLUTION BOX +%================================ + +\makeatletter +\newtcolorbox{solution}{enhanced, + breakable, + colback=white, + colframe=myg!80!black, + attach boxed title to top left={yshift*=-\tcboxedtitleheight}, + title=Solution, + boxed title size=title, + boxed title style={% + sharp corners, + rounded corners=northwest, + colback=tcbcolframe, + boxrule=0pt, + }, + underlay boxed title={% + \path[fill=tcbcolframe] (title.south west)--(title.south east) + to[out=0, in=180] ([xshift=5mm]title.east)-- + (title.center-|frame.east) + [rounded corners=\kvtcb@arc] |- + (frame.north) -| cycle; + }, +} +\makeatother + +%================================ +% Question BOX +%================================ + +\makeatletter +\newtcbtheorem{qstion}{Question}{enhanced, + breakable, + colback=white, + colframe=mygr, + attach boxed title to top left={yshift*=-\tcboxedtitleheight}, + fonttitle=\bfseries, + title={#2}, + boxed title size=title, + boxed title style={% + sharp corners, + rounded corners=northwest, + colback=tcbcolframe, + boxrule=0pt, + }, + underlay boxed title={% + \path[fill=tcbcolframe] (title.south west)--(title.south east) + to[out=0, in=180] ([xshift=5mm]title.east)-- + (title.center-|frame.east) + [rounded corners=\kvtcb@arc] |- + (frame.north) -| cycle; + }, + #1 +}{def} +\makeatother + +\newtcbtheorem[number within=chapter]{wconc}{Wrong Concept}{ + breakable, + enhanced, + colback=white, + colframe=myr, + arc=0pt, + outer arc=0pt, + fonttitle=\bfseries\sffamily\large, + colbacktitle=myr, + attach boxed title to top left={}, + boxed title style={ + enhanced, + skin=enhancedfirst jigsaw, + arc=3pt, + bottom=0pt, + interior style={fill=myr} + }, + #1 +}{def} + + + +%================================ +% NOTE BOX +%================================ + +\usetikzlibrary{arrows,calc,shadows.blur} +\tcbuselibrary{skins} +\newtcolorbox{note}[1][]{% + enhanced jigsaw, + colback=gray!20!white,% + colframe=gray!80!black, + size=small, + boxrule=1pt, + title=\textbf{Note:}, + halign title=flush center, + coltitle=black, + breakable, + drop shadow=black!50!white, + attach boxed title to top left={xshift=1cm,yshift=-\tcboxedtitleheight/2,yshifttext=-\tcboxedtitleheight/2}, + minipage boxed title=1.5cm, + boxed title style={% + colback=white, + size=fbox, + boxrule=1pt, + boxsep=2pt, + underlay={% + \coordinate (dotA) at ($(interior.west) + (-0.5pt,0)$); + \coordinate (dotB) at ($(interior.east) + (0.5pt,0)$); + \begin{scope} + \clip (interior.north west) rectangle ([xshift=3ex]interior.east); + \filldraw [white, blur shadow={shadow opacity=60, shadow yshift=-.75ex}, rounded corners=2pt] (interior.north west) rectangle (interior.south east); + \end{scope} + \begin{scope}[gray!80!black] + \fill (dotA) circle (2pt); + \fill (dotB) circle (2pt); + \end{scope} + }, + }, + #1, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% SELF MADE COMMANDS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\newcommand{\thm}[2]{\begin{Theorem}{#1}{}#2\end{Theorem}} +\newcommand{\cor}[2]{\begin{Corollary}{#1}{}#2\end{Corollary}} +\newcommand{\rvw}[2]{\begin{Review}{#1}{}#2\end{Review}} +\newcommand{\mthd}[2]{\begin{Method}{#1}{}#2\end{Method}} +\newcommand{\clm}[3]{\begin{claim}{#1}{#2}#3\end{claim}} +\newcommand{\wc}[2]{\begin{wconc}{#1}{}\setlength{\parindent}{1cm}#2\end{wconc}} +\newcommand{\thmcon}[1]{\begin{Theoremcon}{#1}\end{Theoremcon}} +\newcommand{\ex}[2]{\begin{Example}{#1}{}#2\end{Example}} +\newcommand{\dfn}[2]{\begin{Definition}[colbacktitle=red!75!black]{#1}{}#2\end{Definition}} +\newcommand{\dfnc}[2]{\begin{definition}[colbacktitle=red!75!black]{#1}{}#2\end{definition}} +\newcommand{\qs}[2]{\begin{question}{#1}{}#2\end{question}} +\newcommand{\pf}[2]{\begin{myproof}[#1]#2\end{myproof}} +\newcommand{\nt}[1]{\begin{note}#1\end{note}} + +\newcommand*\circled[1]{\tikz[baseline=(char.base)]{ + \node[shape=circle,draw,inner sep=1pt] (char) {#1};}} +\newcommand\getcurrentref[1]{% + \ifnumequal{\value{#1}}{0} + {??} + {\the\value{#1}}% +} +\newcommand{\getCurrentSectionNumber}{\getcurrentref{section}} +\newenvironment{myproof}[1][\proofname]{% + \proof[\bfseries #1: ]% +}{\endproof} + +\newcommand{\mclm}[2]{\begin{myclaim}[#1]#2\end{myclaim}} +\newenvironment{myclaim}[1][\claimname]{\proof[\bfseries #1: ]}{} + +\newcounter{mylabelcounter} + +\makeatletter +\newcommand{\setword}[2]{% + \phantomsection + #1\def\@currentlabel{\unexpanded{#1}}\label{#2}% +} +\makeatother + + + + +\tikzset{ + symbol/.style={ + draw=none, + every to/.append style={ + edge node={node [sloped, allow upside down, auto=false]{$#1$}}} + } +} + + +% deliminators +\DeclarePairedDelimiter{\abs}{\lvert}{\rvert} +\DeclarePairedDelimiter{\norm}{\lVert}{\rVert} + +\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil} +\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor} +\DeclarePairedDelimiter{\round}{\lfloor}{\rceil} + +\newsavebox\diffdbox +\newcommand{\slantedromand}{{\mathpalette\makesl{d}}} +\newcommand{\makesl}[2]{% +\begingroup +\sbox{\diffdbox}{$\mathsurround=0pt#1\mathrm{#2}$}% +\pdfsave +\pdfsetmatrix{1 0 0.2 1}% +\rlap{\usebox{\diffdbox}}% +\pdfrestore +\hskip\wd\diffdbox +\endgroup +} +\newcommand{\dd}[1][]{\ensuremath{\mathop{}\!\ifstrempty{#1}{% +\slantedromand\@ifnextchar^{\hspace{0.2ex}}{\hspace{0.1ex}}}% +{\slantedromand\hspace{0.2ex}^{#1}}}} +\ProvideDocumentCommand\dv{o m g}{% + \ensuremath{% + \IfValueTF{#3}{% + \IfNoValueTF{#1}{% + \frac{\dd #2}{\dd #3}% + }{% + \frac{\dd^{#1} #2}{\dd #3^{#1}}% + }% + }{% + \IfNoValueTF{#1}{% + \frac{\dd}{\dd #2}% + }{% + \frac{\dd^{#1}}{\dd #2^{#1}}% + }% + }% + }% +} +\providecommand*{\pdv}[3][]{\frac{\partial^{#1}#2}{\partial#3^{#1}}} +% - others +\DeclareMathOperator{\Lap}{\mathcal{L}} +\DeclareMathOperator{\Var}{Var} % varience +\DeclareMathOperator{\Cov}{Cov} % covarience +\DeclareMathOperator{\E}{E} % expected + +% Since the amsthm package isn't loaded + +% I prefer the slanted \leq +\let\oldleq\leq % save them in case they're every wanted +\let\oldgeq\geq +\renewcommand{\leq}{\leqslant} +\renewcommand{\geq}{\geqslant} + +% % redefine matrix env to allow for alignment, use r as default +% \renewcommand*\env@matrix[1][r]{\hskip -\arraycolsep +% \let\@ifnextchar\new@ifnextchar +% \array{*\c@MaxMatrixCols #1}} + + +%\usepackage{framed} +%\usepackage{titletoc} +%\usepackage{etoolbox} +%\usepackage{lmodern} + + +%\patchcmd{\tableofcontents}{\contentsname}{\sffamily\contentsname}{}{} + +%\renewenvironment{leftbar} +%{\def\FrameCommand{\hspace{6em}% +% {\color{myyellow}\vrule width 2pt depth 6pt}\hspace{1em}}% +% \MakeFramed{\parshape 1 0cm \dimexpr\textwidth-6em\relax\FrameRestore}\vskip2pt% +%} +%{\endMakeFramed} + +%\titlecontents{chapter} +%[0em]{\vspace*{2\baselineskip}} +%{\parbox{4.5em}{% +% \hfill\Huge\sffamily\bfseries\color{myred}\thecontentspage}% +% \vspace*{-2.3\baselineskip}\leftbar\textsc{\small\chaptername~\thecontentslabel}\\\sffamily} +%{}{\endleftbar} +%\titlecontents{section} +%[8.4em] +%{\sffamily\contentslabel{3em}}{}{} +%{\hspace{0.5em}\nobreak\itshape\color{myred}\contentspage} +%\titlecontents{subsection} +%[8.4em] +%{\sffamily\contentslabel{3em}}{}{} +%{\hspace{0.5em}\nobreak\itshape\color{myred}\contentspage} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% TABLE OF CONTENTS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\usepackage{tikz} +\definecolor{doc}{RGB}{0,60,110} +\usepackage{titletoc} +\contentsmargin{0cm} +\titlecontents{chapter}[3.7pc] +{\addvspace{30pt}% + \begin{tikzpicture}[remember picture, overlay]% + \draw[fill=doc!60,draw=doc!60] (-7,-.1) rectangle (-0.9,.5);% + \pgftext[left,x=-3.5cm,y=0.2cm]{\color{white}\Large\sc\bfseries Chapter\ \thecontentslabel};% + \end{tikzpicture}\color{doc!60}\large\sc\bfseries}% +{} +{} +{\;\titlerule\;\large\sc\bfseries Page \thecontentspage + \begin{tikzpicture}[remember picture, overlay] + \draw[fill=doc!60,draw=doc!60] (2pt,0) rectangle (4,0.1pt); + \end{tikzpicture}}% +\titlecontents{section}[3.7pc] +{\addvspace{2pt}} +{\contentslabel[\thecontentslabel]{2pc}} +{} +{\hfill\small \thecontentspage} +[] +\titlecontents*{subsection}[3.7pc] +{\addvspace{-1pt}\small} +{} +{} +{\ --- \small\thecontentspage} +[ \textbullet\ ][] + +\makeatletter +\renewcommand{\tableofcontents}{% + \chapter*{% + \vspace*{-20\p@}% + \begin{tikzpicture}[remember picture, overlay]% + \pgftext[right,x=15cm,y=0.2cm]{\color{doc!60}\Huge\sc\bfseries \contentsname};% + \draw[fill=doc!60,draw=doc!60] (13,-.75) rectangle (20,1);% + \clip (13,-.75) rectangle (20,1); + \pgftext[right,x=15cm,y=0.2cm]{\color{white}\Huge\sc\bfseries \contentsname};% + \end{tikzpicture}}% + \@starttoc{toc}} +\makeatother + diff --git a/6th-Semester-Spring-2024/EnI/engagemnt-hours.wiki b/6th-Semester-Spring-2024/EnI/engagemnt-hours.wiki new file mode 100644 index 0000000..458fa26 --- /dev/null +++ b/6th-Semester-Spring-2024/EnI/engagemnt-hours.wiki @@ -0,0 +1,21 @@ += Engagement Hours Notes = + +== CEO Club ProfTank (Thursday, February 8th, 2024) == +- Caught up on Byron's 3D printing business + - Has been going to shows to promote business + - Meeting lots of people + - Constantly exploring ways to expand and improve +- Met other engineering students taking EnI + - Discussed target markets + - +== Aer Cosmetics Talk (Thursday, February 15th, 2024) == +- Paige DeAngelo shared her story about how she founded Aer Cosmetics + - Always had to figure out financial problems + - Had the idea after realizing that one of her biggest sources of waste was makeup + - Switched from studying meterology to entrepreneurship to pursue this idea +- Aer Cosmetics progress + - Convinced professors to make working on Aer Cosmetics part of final projects + - GSEA startup idea competition + - Started as the first sustainable mascara, eventually competition started + - Competition makes you hone in on your target market + - Goal is line of sustainable cosmetics diff --git a/6th-Semester-Spring-2024/Modules/Notes/letterfonts.tex b/6th-Semester-Spring-2024/Modules/Notes/letterfonts.tex new file mode 100644 index 0000000..e28675f --- /dev/null +++ b/6th-Semester-Spring-2024/Modules/Notes/letterfonts.tex @@ -0,0 +1,178 @@ +% Things Lie +\newcommand{\kb}{\mathfrak b} +\newcommand{\kg}{\mathfrak g} +\newcommand{\kh}{\mathfrak h} +\newcommand{\kn}{\mathfrak n} +\newcommand{\ku}{\mathfrak u} +\newcommand{\kz}{\mathfrak z} +\DeclareMathOperator{\Ext}{Ext} % Ext functor +\DeclareMathOperator{\Tor}{Tor} % Tor functor +\newcommand{\gl}{\opname{\mathfrak{gl}}} % frak gl group +\renewcommand{\sl}{\opname{\mathfrak{sl}}} % frak sl group chktex 6 + +% More script letters etc. +\newcommand{\SA}{\mathcal A} +\newcommand{\SB}{\mathcal B} +\newcommand{\SC}{\mathcal C} +\newcommand{\SF}{\mathcal F} +\newcommand{\SG}{\mathcal G} +\newcommand{\SH}{\mathcal H} +\newcommand{\OO}{\mathcal O} + +\newcommand{\SCA}{\mathscr A} +\newcommand{\SCB}{\mathscr B} +\newcommand{\SCC}{\mathscr C} +\newcommand{\SCD}{\mathscr D} +\newcommand{\SCE}{\mathscr E} +\newcommand{\SCF}{\mathscr F} +\newcommand{\SCG}{\mathscr G} +\newcommand{\SCH}{\mathscr H} + +% Mathfrak primes +\newcommand{\km}{\mathfrak m} +\newcommand{\kp}{\mathfrak p} +\newcommand{\kq}{\mathfrak q} + +% number sets +\newcommand{\RR}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{R}}{\mathbb{R}^{#1}}}} +\newcommand{\NN}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{N}}{\mathbb{N}^{#1}}}} +\newcommand{\ZZ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Z}}{\mathbb{Z}^{#1}}}} +\newcommand{\QQ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Q}}{\mathbb{Q}^{#1}}}} +\newcommand{\CC}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{C}}{\mathbb{C}^{#1}}}} +\newcommand{\PP}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{P}}{\mathbb{P}^{#1}}}} +\newcommand{\HH}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{H}}{\mathbb{H}^{#1}}}} +\newcommand{\FF}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{F}}{\mathbb{F}^{#1}}}} +% expected value +\newcommand{\EE}{\ensuremath{\mathbb{E}}} +\newcommand{\charin}{\text{ char }} +\DeclareMathOperator{\sign}{sign} +\DeclareMathOperator{\Aut}{Aut} +\DeclareMathOperator{\Inn}{Inn} +\DeclareMathOperator{\Syl}{Syl} +\DeclareMathOperator{\Gal}{Gal} +\DeclareMathOperator{\GL}{GL} % General linear group +\DeclareMathOperator{\SL}{SL} % Special linear group + +%--------------------------------------- +% BlackBoard Math Fonts :- +%--------------------------------------- + +%Captital Letters +\newcommand{\bbA}{\mathbb{A}} \newcommand{\bbB}{\mathbb{B}} +\newcommand{\bbC}{\mathbb{C}} \newcommand{\bbD}{\mathbb{D}} +\newcommand{\bbE}{\mathbb{E}} \newcommand{\bbF}{\mathbb{F}} +\newcommand{\bbG}{\mathbb{G}} \newcommand{\bbH}{\mathbb{H}} +\newcommand{\bbI}{\mathbb{I}} \newcommand{\bbJ}{\mathbb{J}} +\newcommand{\bbK}{\mathbb{K}} \newcommand{\bbL}{\mathbb{L}} +\newcommand{\bbM}{\mathbb{M}} \newcommand{\bbN}{\mathbb{N}} +\newcommand{\bbO}{\mathbb{O}} \newcommand{\bbP}{\mathbb{P}} +\newcommand{\bbQ}{\mathbb{Q}} \newcommand{\bbR}{\mathbb{R}} +\newcommand{\bbS}{\mathbb{S}} \newcommand{\bbT}{\mathbb{T}} +\newcommand{\bbU}{\mathbb{U}} \newcommand{\bbV}{\mathbb{V}} +\newcommand{\bbW}{\mathbb{W}} \newcommand{\bbX}{\mathbb{X}} +\newcommand{\bbY}{\mathbb{Y}} \newcommand{\bbZ}{\mathbb{Z}} + +%--------------------------------------- +% MathCal Fonts :- +%--------------------------------------- + +%Captital Letters +\newcommand{\mcA}{\mathcal{A}} \newcommand{\mcB}{\mathcal{B}} +\newcommand{\mcC}{\mathcal{C}} \newcommand{\mcD}{\mathcal{D}} +\newcommand{\mcE}{\mathcal{E}} \newcommand{\mcF}{\mathcal{F}} +\newcommand{\mcG}{\mathcal{G}} \newcommand{\mcH}{\mathcal{H}} +\newcommand{\mcI}{\mathcal{I}} \newcommand{\mcJ}{\mathcal{J}} +\newcommand{\mcK}{\mathcal{K}} \newcommand{\mcL}{\mathcal{L}} +\newcommand{\mcM}{\mathcal{M}} \newcommand{\mcN}{\mathcal{N}} +\newcommand{\mcO}{\mathcal{O}} \newcommand{\mcP}{\mathcal{P}} +\newcommand{\mcQ}{\mathcal{Q}} \newcommand{\mcR}{\mathcal{R}} +\newcommand{\mcS}{\mathcal{S}} \newcommand{\mcT}{\mathcal{T}} +\newcommand{\mcU}{\mathcal{U}} \newcommand{\mcV}{\mathcal{V}} +\newcommand{\mcW}{\mathcal{W}} \newcommand{\mcX}{\mathcal{X}} +\newcommand{\mcY}{\mathcal{Y}} \newcommand{\mcZ}{\mathcal{Z}} + + +%--------------------------------------- +% Bold Math Fonts :- +%--------------------------------------- + +%Captital Letters +\newcommand{\bmA}{\boldsymbol{A}} \newcommand{\bmB}{\boldsymbol{B}} +\newcommand{\bmC}{\boldsymbol{C}} \newcommand{\bmD}{\boldsymbol{D}} +\newcommand{\bmE}{\boldsymbol{E}} \newcommand{\bmF}{\boldsymbol{F}} +\newcommand{\bmG}{\boldsymbol{G}} \newcommand{\bmH}{\boldsymbol{H}} +\newcommand{\bmI}{\boldsymbol{I}} \newcommand{\bmJ}{\boldsymbol{J}} +\newcommand{\bmK}{\boldsymbol{K}} \newcommand{\bmL}{\boldsymbol{L}} +\newcommand{\bmM}{\boldsymbol{M}} \newcommand{\bmN}{\boldsymbol{N}} +\newcommand{\bmO}{\boldsymbol{O}} \newcommand{\bmP}{\boldsymbol{P}} +\newcommand{\bmQ}{\boldsymbol{Q}} \newcommand{\bmR}{\boldsymbol{R}} +\newcommand{\bmS}{\boldsymbol{S}} \newcommand{\bmT}{\boldsymbol{T}} +\newcommand{\bmU}{\boldsymbol{U}} \newcommand{\bmV}{\boldsymbol{V}} +\newcommand{\bmW}{\boldsymbol{W}} \newcommand{\bmX}{\boldsymbol{X}} +\newcommand{\bmY}{\boldsymbol{Y}} \newcommand{\bmZ}{\boldsymbol{Z}} +%Small Letters +\newcommand{\bma}{\boldsymbol{a}} \newcommand{\bmb}{\boldsymbol{b}} +\newcommand{\bmc}{\boldsymbol{c}} \newcommand{\bmd}{\boldsymbol{d}} +\newcommand{\bme}{\boldsymbol{e}} \newcommand{\bmf}{\boldsymbol{f}} +\newcommand{\bmg}{\boldsymbol{g}} \newcommand{\bmh}{\boldsymbol{h}} +\newcommand{\bmi}{\boldsymbol{i}} \newcommand{\bmj}{\boldsymbol{j}} +\newcommand{\bmk}{\boldsymbol{k}} \newcommand{\bml}{\boldsymbol{l}} +\newcommand{\bmm}{\boldsymbol{m}} \newcommand{\bmn}{\boldsymbol{n}} +\newcommand{\bmo}{\boldsymbol{o}} \newcommand{\bmp}{\boldsymbol{p}} +\newcommand{\bmq}{\boldsymbol{q}} \newcommand{\bmr}{\boldsymbol{r}} +\newcommand{\bms}{\boldsymbol{s}} \newcommand{\bmt}{\boldsymbol{t}} +\newcommand{\bmu}{\boldsymbol{u}} \newcommand{\bmv}{\boldsymbol{v}} +\newcommand{\bmw}{\boldsymbol{w}} \newcommand{\bmx}{\boldsymbol{x}} +\newcommand{\bmy}{\boldsymbol{y}} \newcommand{\bmz}{\boldsymbol{z}} + +%--------------------------------------- +% Scr Math Fonts :- +%--------------------------------------- + +\newcommand{\sA}{{\mathscr{A}}} \newcommand{\sB}{{\mathscr{B}}} +\newcommand{\sC}{{\mathscr{C}}} \newcommand{\sD}{{\mathscr{D}}} +\newcommand{\sE}{{\mathscr{E}}} \newcommand{\sF}{{\mathscr{F}}} +\newcommand{\sG}{{\mathscr{G}}} \newcommand{\sH}{{\mathscr{H}}} +\newcommand{\sI}{{\mathscr{I}}} \newcommand{\sJ}{{\mathscr{J}}} +\newcommand{\sK}{{\mathscr{K}}} \newcommand{\sL}{{\mathscr{L}}} +\newcommand{\sM}{{\mathscr{M}}} \newcommand{\sN}{{\mathscr{N}}} +\newcommand{\sO}{{\mathscr{O}}} \newcommand{\sP}{{\mathscr{P}}} +\newcommand{\sQ}{{\mathscr{Q}}} \newcommand{\sR}{{\mathscr{R}}} +\newcommand{\sS}{{\mathscr{S}}} \newcommand{\sT}{{\mathscr{T}}} +\newcommand{\sU}{{\mathscr{U}}} \newcommand{\sV}{{\mathscr{V}}} +\newcommand{\sW}{{\mathscr{W}}} \newcommand{\sX}{{\mathscr{X}}} +\newcommand{\sY}{{\mathscr{Y}}} \newcommand{\sZ}{{\mathscr{Z}}} + + +%--------------------------------------- +% Math Fraktur Font +%--------------------------------------- + +%Captital Letters +\newcommand{\mfA}{\mathfrak{A}} \newcommand{\mfB}{\mathfrak{B}} +\newcommand{\mfC}{\mathfrak{C}} \newcommand{\mfD}{\mathfrak{D}} +\newcommand{\mfE}{\mathfrak{E}} \newcommand{\mfF}{\mathfrak{F}} +\newcommand{\mfG}{\mathfrak{G}} \newcommand{\mfH}{\mathfrak{H}} +\newcommand{\mfI}{\mathfrak{I}} \newcommand{\mfJ}{\mathfrak{J}} +\newcommand{\mfK}{\mathfrak{K}} \newcommand{\mfL}{\mathfrak{L}} +\newcommand{\mfM}{\mathfrak{M}} \newcommand{\mfN}{\mathfrak{N}} +\newcommand{\mfO}{\mathfrak{O}} \newcommand{\mfP}{\mathfrak{P}} +\newcommand{\mfQ}{\mathfrak{Q}} \newcommand{\mfR}{\mathfrak{R}} +\newcommand{\mfS}{\mathfrak{S}} \newcommand{\mfT}{\mathfrak{T}} +\newcommand{\mfU}{\mathfrak{U}} \newcommand{\mfV}{\mathfrak{V}} +\newcommand{\mfW}{\mathfrak{W}} \newcommand{\mfX}{\mathfrak{X}} +\newcommand{\mfY}{\mathfrak{Y}} \newcommand{\mfZ}{\mathfrak{Z}} +%Small Letters +\newcommand{\mfa}{\mathfrak{a}} \newcommand{\mfb}{\mathfrak{b}} +\newcommand{\mfc}{\mathfrak{c}} \newcommand{\mfd}{\mathfrak{d}} +\newcommand{\mfe}{\mathfrak{e}} \newcommand{\mff}{\mathfrak{f}} +\newcommand{\mfg}{\mathfrak{g}} \newcommand{\mfh}{\mathfrak{h}} +\newcommand{\mfi}{\mathfrak{i}} \newcommand{\mfj}{\mathfrak{j}} +\newcommand{\mfk}{\mathfrak{k}} \newcommand{\mfl}{\mathfrak{l}} +\newcommand{\mfm}{\mathfrak{m}} \newcommand{\mfn}{\mathfrak{n}} +\newcommand{\mfo}{\mathfrak{o}} \newcommand{\mfp}{\mathfrak{p}} +\newcommand{\mfq}{\mathfrak{q}} \newcommand{\mfr}{\mathfrak{r}} +\newcommand{\mfs}{\mathfrak{s}} \newcommand{\mft}{\mathfrak{t}} +\newcommand{\mfu}{\mathfrak{u}} \newcommand{\mfv}{\mathfrak{v}} +\newcommand{\mfw}{\mathfrak{w}} \newcommand{\mfx}{\mathfrak{x}} +\newcommand{\mfy}{\mathfrak{y}} \newcommand{\mfz}{\mathfrak{z}} diff --git a/6th-Semester-Spring-2024/Modules/Notes/macros.tex b/6th-Semester-Spring-2024/Modules/Notes/macros.tex new file mode 100644 index 0000000..8bbdb96 --- /dev/null +++ b/6th-Semester-Spring-2024/Modules/Notes/macros.tex @@ -0,0 +1,88 @@ +%From M275 "Topology" at SJSU +\newcommand{\id}{\mathrm{id}} +\newcommand{\taking}[1]{\xrightarrow{#1}} +\newcommand{\inv}{^{-1}} + +%From M170 "Introduction to Graph Theory" at SJSU +\DeclareMathOperator{\diam}{diam} +\DeclareMathOperator{\ord}{ord} +\newcommand{\defeq}{\overset{\mathrm{def}}{=}} + +%From the USAMO .tex files +\newcommand{\ts}{\textsuperscript} +\newcommand{\dg}{^\circ} +\newcommand{\ii}{\item} + +% % From Math 55 and Math 145 at Harvard +% \newenvironment{subproof}[1][Proof]{% +% \begin{proof}[#1] \renewcommand{\qedsymbol}{$\blacksquare$}}% +% {\end{proof}} + +\newcommand{\liff}{\leftrightarrow} +\newcommand{\lthen}{\rightarrow} +\newcommand{\opname}{\operatorname} +\newcommand{\surjto}{\twoheadrightarrow} +\newcommand{\injto}{\hookrightarrow} +\newcommand{\On}{\mathrm{On}} % ordinals +\DeclareMathOperator{\img}{im} % Image +\DeclareMathOperator{\Img}{Im} % Image +\DeclareMathOperator{\coker}{coker} % Cokernel +\DeclareMathOperator{\Coker}{Coker} % Cokernel +\DeclareMathOperator{\Ker}{Ker} % Kernel +\DeclareMathOperator{\rank}{rank} +\DeclareMathOperator{\Spec}{Spec} % spectrum +\DeclareMathOperator{\Tr}{Tr} % trace +\DeclareMathOperator{\pr}{pr} % projection +\DeclareMathOperator{\ext}{ext} % extension +\DeclareMathOperator{\pred}{pred} % predecessor +\DeclareMathOperator{\dom}{dom} % domain +\DeclareMathOperator{\ran}{ran} % range +\DeclareMathOperator{\Hom}{Hom} % homomorphism +\DeclareMathOperator{\Mor}{Mor} % morphisms +\DeclareMathOperator{\End}{End} % endomorphism + +\newcommand{\eps}{\epsilon} +\newcommand{\veps}{\varepsilon} +\newcommand{\ol}{\overline} +\newcommand{\ul}{\underline} +\newcommand{\wt}{\widetilde} +\newcommand{\wh}{\widehat} +\newcommand{\vocab}[1]{\textbf{\color{blue} #1}} +\providecommand{\half}{\frac{1}{2}} +\newcommand{\dang}{\measuredangle} %% Directed angle +\newcommand{\ray}[1]{\overrightarrow{#1}} +\newcommand{\seg}[1]{\overline{#1}} +\newcommand{\arc}[1]{\wideparen{#1}} +\DeclareMathOperator{\cis}{cis} +\DeclareMathOperator*{\lcm}{lcm} +\DeclareMathOperator*{\argmin}{arg min} +\DeclareMathOperator*{\argmax}{arg max} +\newcommand{\cycsum}{\sum_{\mathrm{cyc}}} +\newcommand{\symsum}{\sum_{\mathrm{sym}}} +\newcommand{\cycprod}{\prod_{\mathrm{cyc}}} +\newcommand{\symprod}{\prod_{\mathrm{sym}}} +\newcommand{\Qed}{\begin{flushright}\qed\end{flushright}} +\newcommand{\parinn}{\setlength{\parindent}{1cm}} +\newcommand{\parinf}{\setlength{\parindent}{0cm}} +% \newcommand{\norm}{\|\cdot\|} +\newcommand{\inorm}{\norm_{\infty}} +\newcommand{\opensets}{\{V_{\alpha}\}_{\alpha\in I}} +\newcommand{\oset}{V_{\alpha}} +\newcommand{\opset}[1]{V_{\alpha_{#1}}} +\newcommand{\lub}{\text{lub}} +\newcommand{\del}[2]{\frac{\partial #1}{\partial #2}} +\newcommand{\Del}[3]{\frac{\partial^{#1} #2}{\partial^{#1} #3}} +\newcommand{\deld}[2]{\dfrac{\partial #1}{\partial #2}} +\newcommand{\Deld}[3]{\dfrac{\partial^{#1} #2}{\partial^{#1} #3}} +\newcommand{\lm}{\lambda} +\newcommand{\uin}{\mathbin{\rotatebox[origin=c]{90}{$\in$}}} +\newcommand{\usubset}{\mathbin{\rotatebox[origin=c]{90}{$\subset$}}} +\newcommand{\lt}{\left} +\newcommand{\rt}{\right} +\newcommand{\bs}[1]{\boldsymbol{#1}} +\newcommand{\exs}{\exists} +\newcommand{\st}{\strut} +\newcommand{\dps}[1]{\displaystyle{#1}} + +\newcommand{\sol}{\setlength{\parindent}{0cm}\textbf{\textit{Solution:}}\setlength{\parindent}{1cm} } +\newcommand{\solve}[1]{\setlength{\parindent}{0cm}\textbf{\textit{Solution: }}\setlength{\parindent}{1cm}#1 \Qed} diff --git a/6th-Semester-Spring-2024/Modules/Notes/modules-notes.aux b/6th-Semester-Spring-2024/Modules/Notes/modules-notes.aux new file mode 100644 index 0000000..b4fa28f --- /dev/null +++ b/6th-Semester-Spring-2024/Modules/Notes/modules-notes.aux @@ -0,0 +1,45 @@ +\relax +\providecommand{\transparent@use}[1]{} +\providecommand\hyper@newdestlabel[2]{} +\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} 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b/6th-Semester-Spring-2024/Modules/Notes/modules-notes.tex @@ -0,0 +1,81 @@ +\documentclass{report} + +\input{preamble} +\input{macros} +\input{letterfonts} + +\title{\Huge{Modules in Electrical and Computer Engineering}} +\author{\huge{Aidan Sharpe}} + +\usepackage{circuitikz} + +\begin{document} + +\maketitle +\date{} +\newpage% or \cleardoublepage +% \pdfbookmark[<level>]{<title>}{<dest>} +\pdfbookmark[section]{\contentsname}{toc} +\tableofcontents +\pagebreak + +\chapter{Node Voltage Analysis} +\chapter{Mesh Current Analysis} +While a loop can be any closed path in a circuit, a mesh must be a loop with no loops contained. To perform mesh analysis: +\begin{enumerate} + \item Identify all of the meshes in the circuit + \item Pick a direction to be positive for the currents in the meshes (clockwise or counter-clockwise) + \item Apply Kirchhoff's Voltage Law (KVL), adding voltage increases and subtracting voltage drops. +\end{enumerate} + +\begin{center} +\begin{circuitikz}[american voltages,american inductors] +\draw + (0,3) to [V,l_=$V_1$](0,0) + (4,3) + node[label={above:$\text{V}_{x}$}] {} + to [R,*-*, l^=$R_1$] (4,0) + node[ground] {} + (8,3) to [short] (8,0) + (0,0)--(8,0) + (0,3) to [C, l^=$C_1$] (4,3) + to [L, l^=$L_1$] (8,3); + \draw[->,shift={(2,1.5)}] (120:.7cm) arc (120:-90:.7cm) node at(0,0){$I_1$}; + \draw[->,shift={(6,1.5)}] (120:.7cm) arc (120:-90:.7cm) node at(0,0){$I_2$}; +\end{circuitikz} +\end{center} + + +\nt +{ + It is safe to assume that a resistor will always cause a voltage drop in the direction of the mesh current, but pay attention to what direction voltage sources are oriented. When the current goes from the negative terminal to the positive terminal of a voltage source, add the voltage, but when the current goes from the positive terminal to the negative, subtract the voltage. +} + +\section{Special Cases} + +\subsection{Dependent Sources} + +\subsection{Current Sources} + +\subsection{Super Mesh} +A \emph{super mesh} is created when a current source is shared between two meshes. To perform mesh analysis with super meshes or dependent sources: + +\begin{enumerate} + \item Identify all of the meshes in the circuit + \item Pick a direction to be positive for the currents in the meshes (clockwise or counter-clockwise) + \item If there are any current sources shared between two meshes, temporarily remove it to create a larger mesh. + \item Apply the super mesh constraint + \item Apply Kirchhoff's Voltage Law (KVL), adding voltage increases and subtracting voltage drops. +\end{enumerate} + +\paragraph{The Super Mesh Constraint} +The super mesh constraint is a simple equation that relates a current source shared between two meshes to the mesh currents of those meshes. The super mesh constraint will be of the form: +$$I_s = I_1 - I_2$$ +Where: +\begin{itemize} + \item[$I_s$] is the value of the shared current source + \item[$I_1$] is the mesh current parallel to the current source + \item[$I_2$] is the mesh current anti-parallel to the current source +\end{itemize} + +\end{document} diff --git a/6th-Semester-Spring-2024/Modules/Notes/modules-notes.toc b/6th-Semester-Spring-2024/Modules/Notes/modules-notes.toc new file mode 100644 index 0000000..1672aa7 --- /dev/null +++ b/6th-Semester-Spring-2024/Modules/Notes/modules-notes.toc @@ -0,0 +1,8 @@ +\contentsline {chapter}{\numberline {1}Node Voltage Analysis}{2}{chapter.1}% +\contentsline {chapter}{\numberline {2}Mesh Current Analysis}{3}{chapter.2}% +\contentsline {section}{\numberline {2.1}Special Cases}{3}{section.2.1}% +\contentsline {subsection}{\numberline {2.1.1}Dependent Sources}{3}{subsection.2.1.1}% +\contentsline {subsection}{\numberline {2.1.2}Current Sources}{3}{subsection.2.1.2}% +\contentsline {subsection}{\numberline {2.1.3}Super Mesh}{3}{subsection.2.1.3}% +\contentsline {paragraph}{The Super Mesh Constraint}{4}{section*.2}% +\contentsfinish diff --git a/6th-Semester-Spring-2024/Modules/Notes/preamble.tex b/6th-Semester-Spring-2024/Modules/Notes/preamble.tex new file mode 100644 index 0000000..af7d68e --- /dev/null +++ b/6th-Semester-Spring-2024/Modules/Notes/preamble.tex @@ -0,0 +1,779 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PACKAGE IMPORTS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\usepackage[tmargin=2cm,rmargin=1in,lmargin=1in,margin=0.85in,bmargin=2cm,footskip=.2in]{geometry} +\usepackage{amsmath,amsfonts,amsthm,amssymb,mathtools} +\usepackage{listings} +\usepackage[varbb]{newpxmath} +\usepackage{xfrac} +\usepackage[makeroom]{cancel} +\usepackage{mathtools} +\usepackage{bookmark} +\usepackage{enumitem} +\usepackage{hyperref,theoremref} +\hypersetup{ + pdftitle={Assignment}, + colorlinks=true, linkcolor=doc!90, + bookmarksnumbered=true, + 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boxrule = 0sp, + borderline west = {2pt}{0pt}{myexercisefg}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = myexercisefg, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, myexercisefg}, +} +{th} + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=chapter]{exercise}{Exercise} +{% + enhanced, + breakable, + colback = myexercisebg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{myexercisefg}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = myexercisefg, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, myexercisefg}, +} +{th} + +%================================ +% EXAMPLE BOX +%================================ + +\newtcbtheorem[number within=section]{Example}{Example} +{% + colback = myexamplebg + ,breakable + ,colframe = myexamplefr + ,coltitle = myexampleti + ,boxrule = 1pt + ,sharp corners + ,detach title + ,before upper=\tcbtitle\par\smallskip + ,fonttitle = \bfseries + ,description font = \mdseries + ,separator sign none + ,description delimiters parenthesis +} +{ex} + +\newtcbtheorem[number within=chapter]{example}{Example} +{% + colback = myexamplebg + ,breakable + ,colframe = myexamplefr + ,coltitle = myexampleti + ,boxrule = 1pt + ,sharp corners + ,detach title + ,before upper=\tcbtitle\par\smallskip + ,fonttitle = \bfseries + ,description font = \mdseries + ,separator sign none + ,description delimiters parenthesis +} +{ex} + +%================================ +% DEFINITION BOX +%================================ + +\newtcbtheorem[number within=section]{Definition}{Definition}{enhanced, + before skip=2mm,after skip=2mm, colback=red!5,colframe=red!80!black,boxrule=0.5mm, + attach boxed title to top left={xshift=1cm,yshift*=1mm-\tcboxedtitleheight}, varwidth boxed title*=-3cm, + boxed title style={frame code={ + \path[fill=tcbcolback] + ([yshift=-1mm,xshift=-1mm]frame.north west) + arc[start angle=0,end angle=180,radius=1mm] + ([yshift=-1mm,xshift=1mm]frame.north east) + arc[start angle=180,end angle=0,radius=1mm]; + \path[left color=tcbcolback!60!black,right color=tcbcolback!60!black, + middle color=tcbcolback!80!black] + ([xshift=-2mm]frame.north west) -- ([xshift=2mm]frame.north east) + [rounded corners=1mm]-- ([xshift=1mm,yshift=-1mm]frame.north east) + -- (frame.south east) -- (frame.south west) + -- ([xshift=-1mm,yshift=-1mm]frame.north west) + [sharp corners]-- cycle; + },interior engine=empty, + }, + fonttitle=\bfseries, + title={#2},#1}{def} +\newtcbtheorem[number within=chapter]{definition}{Definition}{enhanced, + before skip=2mm,after skip=2mm, colback=red!5,colframe=red!80!black,boxrule=0.5mm, + attach boxed title to top left={xshift=1cm,yshift*=1mm-\tcboxedtitleheight}, varwidth boxed title*=-3cm, + boxed title style={frame code={ + \path[fill=tcbcolback] + ([yshift=-1mm,xshift=-1mm]frame.north west) + arc[start angle=0,end angle=180,radius=1mm] + ([yshift=-1mm,xshift=1mm]frame.north east) + arc[start angle=180,end angle=0,radius=1mm]; + \path[left color=tcbcolback!60!black,right color=tcbcolback!60!black, + middle color=tcbcolback!80!black] + ([xshift=-2mm]frame.north west) -- ([xshift=2mm]frame.north east) + [rounded corners=1mm]-- ([xshift=1mm,yshift=-1mm]frame.north east) + -- (frame.south east) -- (frame.south west) + -- ([xshift=-1mm,yshift=-1mm]frame.north west) + [sharp corners]-- cycle; + },interior engine=empty, + }, + fonttitle=\bfseries, + title={#2},#1}{def} + + + +%================================ +% Solution BOX +%================================ + +\makeatletter +\newtcbtheorem{question}{Question}{enhanced, + breakable, + colback=white, + colframe=myb!80!black, + attach boxed title to top left={yshift*=-\tcboxedtitleheight}, + fonttitle=\bfseries, + title={#2}, + boxed title size=title, + boxed title style={% + sharp corners, + rounded corners=northwest, + colback=tcbcolframe, + boxrule=0pt, + }, + underlay boxed title={% + \path[fill=tcbcolframe] (title.south west)--(title.south east) + to[out=0, in=180] ([xshift=5mm]title.east)-- + (title.center-|frame.east) + [rounded corners=\kvtcb@arc] |- + (frame.north) -| cycle; + }, + #1 +}{def} +\makeatother + +%================================ +% SOLUTION BOX +%================================ + +\makeatletter +\newtcolorbox{solution}{enhanced, + breakable, + colback=white, + colframe=myg!80!black, + attach boxed title to top left={yshift*=-\tcboxedtitleheight}, + title=Solution, + boxed title size=title, + boxed title style={% + sharp corners, + rounded corners=northwest, + colback=tcbcolframe, + boxrule=0pt, + }, + underlay boxed title={% + \path[fill=tcbcolframe] (title.south west)--(title.south east) + to[out=0, in=180] ([xshift=5mm]title.east)-- + (title.center-|frame.east) + [rounded corners=\kvtcb@arc] |- + (frame.north) -| cycle; + }, +} +\makeatother + +%================================ +% Question BOX +%================================ + +\makeatletter +\newtcbtheorem{qstion}{Question}{enhanced, + breakable, + colback=white, + colframe=mygr, + attach boxed title to top left={yshift*=-\tcboxedtitleheight}, + fonttitle=\bfseries, + title={#2}, + boxed title size=title, + boxed title style={% + sharp corners, + rounded corners=northwest, + colback=tcbcolframe, + boxrule=0pt, + }, + underlay boxed title={% + \path[fill=tcbcolframe] (title.south west)--(title.south east) + to[out=0, in=180] ([xshift=5mm]title.east)-- + (title.center-|frame.east) + [rounded corners=\kvtcb@arc] |- + (frame.north) -| cycle; + }, + #1 +}{def} +\makeatother + +\newtcbtheorem[number within=chapter]{wconc}{Wrong Concept}{ + breakable, + enhanced, + colback=white, + colframe=myr, + arc=0pt, + outer arc=0pt, + fonttitle=\bfseries\sffamily\large, + colbacktitle=myr, + attach boxed title to top left={}, + boxed title style={ + enhanced, + skin=enhancedfirst jigsaw, + arc=3pt, + bottom=0pt, + interior style={fill=myr} + }, + #1 +}{def} + + + +%================================ +% NOTE BOX +%================================ + +\usetikzlibrary{arrows,calc,shadows.blur} +\tcbuselibrary{skins} +\newtcolorbox{note}[1][]{% + enhanced jigsaw, + colback=gray!20!white,% + colframe=gray!80!black, + size=small, + boxrule=1pt, + title=\textbf{Note:}, + halign title=flush center, + coltitle=black, + breakable, + drop shadow=black!50!white, + attach boxed title to top left={xshift=1cm,yshift=-\tcboxedtitleheight/2,yshifttext=-\tcboxedtitleheight/2}, + minipage boxed title=1.5cm, + boxed title style={% + colback=white, + size=fbox, + boxrule=1pt, + boxsep=2pt, + underlay={% + \coordinate (dotA) at ($(interior.west) + (-0.5pt,0)$); + \coordinate (dotB) at ($(interior.east) + (0.5pt,0)$); + \begin{scope} + \clip (interior.north west) rectangle ([xshift=3ex]interior.east); + \filldraw [white, blur shadow={shadow opacity=60, shadow yshift=-.75ex}, rounded corners=2pt] (interior.north west) rectangle (interior.south east); + \end{scope} + \begin{scope}[gray!80!black] + \fill (dotA) circle (2pt); + \fill (dotB) circle (2pt); + \end{scope} + }, + }, + #1, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% SELF MADE COMMANDS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\newcommand{\thm}[2]{\begin{Theorem}{#1}{}#2\end{Theorem}} +\newcommand{\cor}[2]{\begin{Corollary}{#1}{}#2\end{Corollary}} +\newcommand{\rvw}[2]{\begin{Review}{#1}{}#2\end{Review}} +\newcommand{\mthd}[2]{\begin{Method}{#1}{}#2\end{Method}} +\newcommand{\clm}[3]{\begin{claim}{#1}{#2}#3\end{claim}} +\newcommand{\wc}[2]{\begin{wconc}{#1}{}\setlength{\parindent}{1cm}#2\end{wconc}} +\newcommand{\thmcon}[1]{\begin{Theoremcon}{#1}\end{Theoremcon}} +\newcommand{\ex}[2]{\begin{Example}{#1}{}#2\end{Example}} +\newcommand{\dfn}[2]{\begin{Definition}[colbacktitle=red!75!black]{#1}{}#2\end{Definition}} +\newcommand{\dfnc}[2]{\begin{definition}[colbacktitle=red!75!black]{#1}{}#2\end{definition}} +\newcommand{\qs}[2]{\begin{question}{#1}{}#2\end{question}} +\newcommand{\pf}[2]{\begin{myproof}[#1]#2\end{myproof}} +\newcommand{\nt}[1]{\begin{note}#1\end{note}} + +\newcommand*\circled[1]{\tikz[baseline=(char.base)]{ + \node[shape=circle,draw,inner sep=1pt] (char) {#1};}} +\newcommand\getcurrentref[1]{% + \ifnumequal{\value{#1}}{0} + {??} + {\the\value{#1}}% +} +\newcommand{\getCurrentSectionNumber}{\getcurrentref{section}} +\newenvironment{myproof}[1][\proofname]{% + \proof[\bfseries #1: ]% +}{\endproof} + +\newcommand{\mclm}[2]{\begin{myclaim}[#1]#2\end{myclaim}} +\newenvironment{myclaim}[1][\claimname]{\proof[\bfseries #1: ]}{} + +\newcounter{mylabelcounter} + +\makeatletter +\newcommand{\setword}[2]{% + \phantomsection + #1\def\@currentlabel{\unexpanded{#1}}\label{#2}% +} +\makeatother + + + + +\tikzset{ + symbol/.style={ + draw=none, + every to/.append style={ + edge node={node [sloped, allow upside down, auto=false]{$#1$}}} + } +} + + +% deliminators +\DeclarePairedDelimiter{\abs}{\lvert}{\rvert} +\DeclarePairedDelimiter{\norm}{\lVert}{\rVert} + +\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil} +\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor} +\DeclarePairedDelimiter{\round}{\lfloor}{\rceil} + +\newsavebox\diffdbox +\newcommand{\slantedromand}{{\mathpalette\makesl{d}}} +\newcommand{\makesl}[2]{% +\begingroup +\sbox{\diffdbox}{$\mathsurround=0pt#1\mathrm{#2}$}% +\pdfsave +\pdfsetmatrix{1 0 0.2 1}% +\rlap{\usebox{\diffdbox}}% +\pdfrestore +\hskip\wd\diffdbox +\endgroup +} +\newcommand{\dd}[1][]{\ensuremath{\mathop{}\!\ifstrempty{#1}{% +\slantedromand\@ifnextchar^{\hspace{0.2ex}}{\hspace{0.1ex}}}% +{\slantedromand\hspace{0.2ex}^{#1}}}} +\ProvideDocumentCommand\dv{o m g}{% + \ensuremath{% + \IfValueTF{#3}{% + \IfNoValueTF{#1}{% + \frac{\dd #2}{\dd #3}% + }{% + \frac{\dd^{#1} #2}{\dd #3^{#1}}% + }% + }{% + \IfNoValueTF{#1}{% + \frac{\dd}{\dd #2}% + }{% + \frac{\dd^{#1}}{\dd #2^{#1}}% + }% + }% + }% +} +\providecommand*{\pdv}[3][]{\frac{\partial^{#1}#2}{\partial#3^{#1}}} +% - others +\DeclareMathOperator{\Lap}{\mathcal{L}} +\DeclareMathOperator{\Var}{Var} % varience +\DeclareMathOperator{\Cov}{Cov} % covarience +\DeclareMathOperator{\E}{E} % expected + +% Since the amsthm package isn't loaded + +% I prefer the slanted \leq +\let\oldleq\leq % save them in case they're every wanted +\let\oldgeq\geq +\renewcommand{\leq}{\leqslant} +\renewcommand{\geq}{\geqslant} + +% % redefine matrix env to allow for alignment, use r as default +% \renewcommand*\env@matrix[1][r]{\hskip -\arraycolsep +% \let\@ifnextchar\new@ifnextchar +% \array{*\c@MaxMatrixCols #1}} + + +%\usepackage{framed} +%\usepackage{titletoc} +%\usepackage{etoolbox} +%\usepackage{lmodern} + + +%\patchcmd{\tableofcontents}{\contentsname}{\sffamily\contentsname}{}{} + +%\renewenvironment{leftbar} +%{\def\FrameCommand{\hspace{6em}% +% {\color{myyellow}\vrule width 2pt depth 6pt}\hspace{1em}}% +% \MakeFramed{\parshape 1 0cm \dimexpr\textwidth-6em\relax\FrameRestore}\vskip2pt% +%} +%{\endMakeFramed} + +%\titlecontents{chapter} +%[0em]{\vspace*{2\baselineskip}} +%{\parbox{4.5em}{% +% \hfill\Huge\sffamily\bfseries\color{myred}\thecontentspage}% +% \vspace*{-2.3\baselineskip}\leftbar\textsc{\small\chaptername~\thecontentslabel}\\\sffamily} +%{}{\endleftbar} +%\titlecontents{section} +%[8.4em] +%{\sffamily\contentslabel{3em}}{}{} +%{\hspace{0.5em}\nobreak\itshape\color{myred}\contentspage} +%\titlecontents{subsection} +%[8.4em] +%{\sffamily\contentslabel{3em}}{}{} +%{\hspace{0.5em}\nobreak\itshape\color{myred}\contentspage} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% TABLE OF CONTENTS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\usepackage{tikz} +\definecolor{doc}{RGB}{0,60,110} +\usepackage{titletoc} +\contentsmargin{0cm} +\titlecontents{chapter}[3.7pc] +{\addvspace{30pt}% + \begin{tikzpicture}[remember picture, overlay]% + \draw[fill=doc!60,draw=doc!60] (-7,-.1) rectangle (-0.9,.5);% + \pgftext[left,x=-3.5cm,y=0.2cm]{\color{white}\Large\sc\bfseries Chapter\ \thecontentslabel};% + \end{tikzpicture}\color{doc!60}\large\sc\bfseries}% +{} +{} +{\;\titlerule\;\large\sc\bfseries Page \thecontentspage + \begin{tikzpicture}[remember picture, overlay] + \draw[fill=doc!60,draw=doc!60] (2pt,0) rectangle (4,0.1pt); + \end{tikzpicture}}% +\titlecontents{section}[3.7pc] +{\addvspace{2pt}} +{\contentslabel[\thecontentslabel]{2pc}} +{} +{\hfill\small \thecontentspage} +[] +\titlecontents*{subsection}[3.7pc] +{\addvspace{-1pt}\small} +{} +{} +{\ --- \small\thecontentspage} +[ \textbullet\ ][] + +\makeatletter +\renewcommand{\tableofcontents}{% + \chapter*{% + \vspace*{-20\p@}% + \begin{tikzpicture}[remember picture, overlay]% + \pgftext[right,x=15cm,y=0.2cm]{\color{doc!60}\Huge\sc\bfseries \contentsname};% + \draw[fill=doc!60,draw=doc!60] (13,-.75) rectangle (20,1);% + \clip (13,-.75) rectangle (20,1); + \pgftext[right,x=15cm,y=0.2cm]{\color{white}\Huge\sc\bfseries \contentsname};% + \end{tikzpicture}}% + \@starttoc{toc}} +\makeatother + diff --git a/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-1/Homework_1-1.pdf b/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-1/Homework_1-1.pdf new file mode 100644 index 0000000..d6cec79 Binary files /dev/null and b/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-1/Homework_1-1.pdf differ diff --git a/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-1/homework-1.aux b/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-1/homework-1.aux new file mode 100644 index 0000000..7b9c896 --- /dev/null +++ b/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-1/homework-1.aux @@ -0,0 +1,9 @@ +\relax +\@writefile{toc}{\contentsline {section}{\numberline {1}Initial Circuit}{1}{}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {2}Diode is 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a/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-1/homework-1.tex b/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-1/homework-1.tex new file mode 100644 index 0000000..d9a6b7d --- /dev/null +++ b/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-1/homework-1.tex @@ -0,0 +1,93 @@ +\documentclass{article} + +\title{Power Electronics Homework 1} +\author{Aidan Sharpe} + +\usepackage{circuitikz} +\usepackage{amsmath} +\usepackage{listings} + +\begin{document} +\maketitle +\date{} + +\section{Initial Circuit} +\begin{center} +\begin{circuitikz}[american voltages] +\draw +(0,0) to [short] (1,0) to [empty diode, l=$D_1$] (3,0) to [open, v=$V_d$] (3,-2) +(3,0) to [short, american inductor, l=$L_1$, i=$i_L$] (6,0) +to [short, american resistor, l_=$R_1$, v^=$V_R$] (6,-2) +to [short] (0,-2) +(0,0) to [vsourcesin, v_=$V_s$] (0,-2); +\end{circuitikz} +\end{center} + +$$V_s(t) = 110 \sqrt{2} \cos(2\pi f t)$$ +$$f = 60 \text{[Hz]}$$ +$$L_1 = 20 \text{[mH]}$$ +$$R_1 = 10 [\Omega]$$ + +\section{Diode is "On"} +\begin{center} +\begin{circuitikz}[american voltages] +\draw +(0,0) to [closing switch] (3,0) to [open, v=$V_d$] (3,-2) +(3,0) to [short, american inductor, l=$L_1$, i=$i_L$] (6,0) +to [short, american resistor, l_=$R_1$, v^=$V_R$] (6,-2) +to [short] (0,-2) +(0,0) to [vsourcesin, v_=$V_s$] (0,-2); +\end{circuitikz} +\end{center} + +$$V_d(t) = V_s(t) = V_L(t) + V_R(t)$$ +$$V_L(t) = L_1 {d \over dt}i_L(t)$$ +$$V_R(t) = R_1 i_L(t)$$ +$$110 \sqrt{2} \cos(120\pi t) = 10 i_L(t) + 0.02 {d\over dt}i_L(t)$$ +Apply Laplace Transform: +$$10 I_L(s) + 0.02 s I_L(s) + i_L(0) = {110 \sqrt{2} s \over 14400 \pi^2 + s^2}$$ +Solve for $I_L(s)$: +$$I_L(s) (10 + 0.02 s) = {110 \sqrt{2} s \over 14400 \pi^2 + s^2}$$ +$$I_L(s) = \frac{110\,\sqrt{2}\,s}{\left(\frac{s}{50}+10\right)\,\left(s^2+14400\,\pi ^2\right)}$$ +Apply Inverse Laplace Transform: +$$i_L(t) = \frac{6875\,\sqrt{2}\,\cos\left(120\,\pi \,t\right)+1650\,\pi \,\sqrt{2}\,\sin\left(120\,\pi \,t\right)}{36\,\pi ^2+625}-\frac{6875\,\sqrt{2}\,{\mathrm{e}}^{-500\,t}}{36\,\pi ^2+625}$$ +$$V_R = \frac{10\,\left(6875\,\sqrt{2}\,\cos\left(120\,\pi \,t\right)+1650\,\pi \,\sqrt{2}\,\sin\left(120\,\pi \,t\right)\right)}{36\,\pi ^2+625}-\frac{68750\,\sqrt{2}\,{\mathrm{e}}^{-500\,t}}{36\,\pi ^2+625}$$ + + +\section{Diode Is "Off"} +\begin{center} +\begin{circuitikz}[american voltages] +\draw +(0,0) to [opening switch] (3,0) to [open, v=$V_d$] (3,-2) +(3,0) to [short, american inductor, l=$L_1$, i=$i_L$] (6,0) +to [short, american resistor, l_=$R_1$, v^=$V_R$] (6,-2) +to [short] (0,-2) +(0,0) to [vsourcesin, v_=$V_s$] (0,-2); +\end{circuitikz} +\end{center} + +\section{LTSpice} +\begin{figure}[h] + \includegraphics[width=\textwidth]{simulation.png} +\end{figure} + +\section{MATLAB} +\begin{lstlisting}[language=MATLAB] +syms s t +R_1 = 10; +L_1 = 0.02; +v_s = 110*sqrt(2)*cos(120*pi*t); + +V_s = laplace(v_s); +I_L = V_s / (R_1 + s*L_1); +i_L = ilaplace(I_L); + +v_o = i_L * R_1 +\end{lstlisting} + +\section{Large Inductor} +As the inductor gets proportionally larger than the resistor, the amplitude of the output voltage decreases and the phase shift increases. +\section{Large Resistor} +As the resistor gets proportionally larger than the inductor, the amplitude of the output approaches the amplitude of the input and the phase shift goes to zero. + +\end{document} diff --git a/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-1/simulation.png b/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-1/simulation.png new file mode 100644 index 0000000..05a8c95 Binary files /dev/null and b/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-1/simulation.png differ diff --git a/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-2/homework-1.aux b/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-2/homework-1.aux new file mode 100644 index 0000000..7b9c896 --- /dev/null +++ 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a/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-2/homework-1.tex b/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-2/homework-1.tex new file mode 100644 index 0000000..d9a6b7d --- /dev/null +++ b/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-2/homework-1.tex @@ -0,0 +1,93 @@ +\documentclass{article} + +\title{Power Electronics Homework 1} +\author{Aidan Sharpe} + +\usepackage{circuitikz} +\usepackage{amsmath} +\usepackage{listings} + +\begin{document} +\maketitle +\date{} + +\section{Initial Circuit} +\begin{center} +\begin{circuitikz}[american voltages] +\draw +(0,0) to [short] (1,0) to [empty diode, l=$D_1$] (3,0) to [open, v=$V_d$] (3,-2) +(3,0) to [short, american inductor, l=$L_1$, i=$i_L$] (6,0) +to [short, american resistor, l_=$R_1$, v^=$V_R$] (6,-2) +to [short] (0,-2) +(0,0) to [vsourcesin, v_=$V_s$] (0,-2); +\end{circuitikz} +\end{center} + +$$V_s(t) = 110 \sqrt{2} \cos(2\pi f t)$$ +$$f = 60 \text{[Hz]}$$ +$$L_1 = 20 \text{[mH]}$$ +$$R_1 = 10 [\Omega]$$ + +\section{Diode is "On"} +\begin{center} +\begin{circuitikz}[american voltages] +\draw +(0,0) to [closing switch] (3,0) to [open, v=$V_d$] (3,-2) +(3,0) to [short, american inductor, l=$L_1$, i=$i_L$] (6,0) +to [short, american resistor, l_=$R_1$, v^=$V_R$] (6,-2) +to [short] (0,-2) +(0,0) to [vsourcesin, v_=$V_s$] (0,-2); +\end{circuitikz} +\end{center} + +$$V_d(t) = V_s(t) = V_L(t) + V_R(t)$$ +$$V_L(t) = L_1 {d \over dt}i_L(t)$$ +$$V_R(t) = R_1 i_L(t)$$ +$$110 \sqrt{2} \cos(120\pi t) = 10 i_L(t) + 0.02 {d\over dt}i_L(t)$$ +Apply Laplace Transform: +$$10 I_L(s) + 0.02 s I_L(s) + i_L(0) = {110 \sqrt{2} s \over 14400 \pi^2 + s^2}$$ +Solve for $I_L(s)$: +$$I_L(s) (10 + 0.02 s) = {110 \sqrt{2} s \over 14400 \pi^2 + s^2}$$ +$$I_L(s) = \frac{110\,\sqrt{2}\,s}{\left(\frac{s}{50}+10\right)\,\left(s^2+14400\,\pi ^2\right)}$$ +Apply Inverse Laplace Transform: +$$i_L(t) = \frac{6875\,\sqrt{2}\,\cos\left(120\,\pi \,t\right)+1650\,\pi \,\sqrt{2}\,\sin\left(120\,\pi \,t\right)}{36\,\pi ^2+625}-\frac{6875\,\sqrt{2}\,{\mathrm{e}}^{-500\,t}}{36\,\pi ^2+625}$$ +$$V_R = \frac{10\,\left(6875\,\sqrt{2}\,\cos\left(120\,\pi \,t\right)+1650\,\pi \,\sqrt{2}\,\sin\left(120\,\pi \,t\right)\right)}{36\,\pi ^2+625}-\frac{68750\,\sqrt{2}\,{\mathrm{e}}^{-500\,t}}{36\,\pi ^2+625}$$ + + +\section{Diode Is "Off"} +\begin{center} +\begin{circuitikz}[american voltages] +\draw +(0,0) to [opening switch] (3,0) to [open, v=$V_d$] (3,-2) +(3,0) to [short, american inductor, l=$L_1$, i=$i_L$] (6,0) +to [short, american resistor, l_=$R_1$, v^=$V_R$] (6,-2) +to [short] (0,-2) +(0,0) to [vsourcesin, v_=$V_s$] (0,-2); +\end{circuitikz} +\end{center} + +\section{LTSpice} +\begin{figure}[h] + \includegraphics[width=\textwidth]{simulation.png} +\end{figure} + +\section{MATLAB} +\begin{lstlisting}[language=MATLAB] +syms s t +R_1 = 10; +L_1 = 0.02; +v_s = 110*sqrt(2)*cos(120*pi*t); + +V_s = laplace(v_s); +I_L = V_s / (R_1 + s*L_1); +i_L = ilaplace(I_L); + +v_o = i_L * R_1 +\end{lstlisting} + +\section{Large Inductor} +As the inductor gets proportionally larger than the resistor, the amplitude of the output voltage decreases and the phase shift increases. +\section{Large Resistor} +As the resistor gets proportionally larger than the inductor, the amplitude of the output approaches the amplitude of the input and the phase shift goes to zero. + +\end{document} diff --git a/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-2/simulation.png b/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-2/simulation.png new file mode 100644 index 0000000..05a8c95 Binary files /dev/null and b/6th-Semester-Spring-2024/Power-Electronics/Homework/Homework-2/simulation.png differ diff --git a/6th-Semester-Spring-2024/Power-Electronics/Notes/letterfonts.tex b/6th-Semester-Spring-2024/Power-Electronics/Notes/letterfonts.tex new file mode 100644 index 0000000..e28675f --- /dev/null +++ b/6th-Semester-Spring-2024/Power-Electronics/Notes/letterfonts.tex @@ -0,0 +1,178 @@ +% Things Lie +\newcommand{\kb}{\mathfrak b} +\newcommand{\kg}{\mathfrak g} +\newcommand{\kh}{\mathfrak h} +\newcommand{\kn}{\mathfrak n} +\newcommand{\ku}{\mathfrak u} +\newcommand{\kz}{\mathfrak z} +\DeclareMathOperator{\Ext}{Ext} % Ext functor +\DeclareMathOperator{\Tor}{Tor} % Tor functor +\newcommand{\gl}{\opname{\mathfrak{gl}}} % frak gl group +\renewcommand{\sl}{\opname{\mathfrak{sl}}} % frak sl group chktex 6 + +% More script letters etc. +\newcommand{\SA}{\mathcal A} +\newcommand{\SB}{\mathcal B} +\newcommand{\SC}{\mathcal C} +\newcommand{\SF}{\mathcal F} +\newcommand{\SG}{\mathcal G} +\newcommand{\SH}{\mathcal H} +\newcommand{\OO}{\mathcal O} + +\newcommand{\SCA}{\mathscr A} +\newcommand{\SCB}{\mathscr B} +\newcommand{\SCC}{\mathscr C} +\newcommand{\SCD}{\mathscr D} +\newcommand{\SCE}{\mathscr E} +\newcommand{\SCF}{\mathscr F} +\newcommand{\SCG}{\mathscr G} +\newcommand{\SCH}{\mathscr H} + +% Mathfrak primes +\newcommand{\km}{\mathfrak m} +\newcommand{\kp}{\mathfrak p} +\newcommand{\kq}{\mathfrak q} + +% number sets +\newcommand{\RR}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{R}}{\mathbb{R}^{#1}}}} +\newcommand{\NN}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{N}}{\mathbb{N}^{#1}}}} +\newcommand{\ZZ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Z}}{\mathbb{Z}^{#1}}}} +\newcommand{\QQ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Q}}{\mathbb{Q}^{#1}}}} +\newcommand{\CC}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{C}}{\mathbb{C}^{#1}}}} +\newcommand{\PP}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{P}}{\mathbb{P}^{#1}}}} +\newcommand{\HH}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{H}}{\mathbb{H}^{#1}}}} +\newcommand{\FF}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{F}}{\mathbb{F}^{#1}}}} +% expected value +\newcommand{\EE}{\ensuremath{\mathbb{E}}} +\newcommand{\charin}{\text{ char }} +\DeclareMathOperator{\sign}{sign} +\DeclareMathOperator{\Aut}{Aut} +\DeclareMathOperator{\Inn}{Inn} +\DeclareMathOperator{\Syl}{Syl} +\DeclareMathOperator{\Gal}{Gal} +\DeclareMathOperator{\GL}{GL} % General linear group +\DeclareMathOperator{\SL}{SL} % Special linear group + +%--------------------------------------- +% BlackBoard Math Fonts :- +%--------------------------------------- + +%Captital Letters +\newcommand{\bbA}{\mathbb{A}} \newcommand{\bbB}{\mathbb{B}} +\newcommand{\bbC}{\mathbb{C}} \newcommand{\bbD}{\mathbb{D}} +\newcommand{\bbE}{\mathbb{E}} \newcommand{\bbF}{\mathbb{F}} +\newcommand{\bbG}{\mathbb{G}} \newcommand{\bbH}{\mathbb{H}} +\newcommand{\bbI}{\mathbb{I}} \newcommand{\bbJ}{\mathbb{J}} +\newcommand{\bbK}{\mathbb{K}} \newcommand{\bbL}{\mathbb{L}} +\newcommand{\bbM}{\mathbb{M}} \newcommand{\bbN}{\mathbb{N}} +\newcommand{\bbO}{\mathbb{O}} \newcommand{\bbP}{\mathbb{P}} +\newcommand{\bbQ}{\mathbb{Q}} \newcommand{\bbR}{\mathbb{R}} +\newcommand{\bbS}{\mathbb{S}} \newcommand{\bbT}{\mathbb{T}} +\newcommand{\bbU}{\mathbb{U}} \newcommand{\bbV}{\mathbb{V}} +\newcommand{\bbW}{\mathbb{W}} \newcommand{\bbX}{\mathbb{X}} +\newcommand{\bbY}{\mathbb{Y}} \newcommand{\bbZ}{\mathbb{Z}} + +%--------------------------------------- +% MathCal Fonts :- +%--------------------------------------- + +%Captital Letters +\newcommand{\mcA}{\mathcal{A}} \newcommand{\mcB}{\mathcal{B}} +\newcommand{\mcC}{\mathcal{C}} \newcommand{\mcD}{\mathcal{D}} +\newcommand{\mcE}{\mathcal{E}} \newcommand{\mcF}{\mathcal{F}} +\newcommand{\mcG}{\mathcal{G}} \newcommand{\mcH}{\mathcal{H}} +\newcommand{\mcI}{\mathcal{I}} \newcommand{\mcJ}{\mathcal{J}} +\newcommand{\mcK}{\mathcal{K}} \newcommand{\mcL}{\mathcal{L}} +\newcommand{\mcM}{\mathcal{M}} \newcommand{\mcN}{\mathcal{N}} +\newcommand{\mcO}{\mathcal{O}} \newcommand{\mcP}{\mathcal{P}} +\newcommand{\mcQ}{\mathcal{Q}} \newcommand{\mcR}{\mathcal{R}} +\newcommand{\mcS}{\mathcal{S}} \newcommand{\mcT}{\mathcal{T}} +\newcommand{\mcU}{\mathcal{U}} \newcommand{\mcV}{\mathcal{V}} +\newcommand{\mcW}{\mathcal{W}} \newcommand{\mcX}{\mathcal{X}} +\newcommand{\mcY}{\mathcal{Y}} \newcommand{\mcZ}{\mathcal{Z}} + + +%--------------------------------------- +% Bold Math Fonts :- +%--------------------------------------- + +%Captital Letters +\newcommand{\bmA}{\boldsymbol{A}} \newcommand{\bmB}{\boldsymbol{B}} +\newcommand{\bmC}{\boldsymbol{C}} \newcommand{\bmD}{\boldsymbol{D}} +\newcommand{\bmE}{\boldsymbol{E}} \newcommand{\bmF}{\boldsymbol{F}} +\newcommand{\bmG}{\boldsymbol{G}} \newcommand{\bmH}{\boldsymbol{H}} +\newcommand{\bmI}{\boldsymbol{I}} \newcommand{\bmJ}{\boldsymbol{J}} +\newcommand{\bmK}{\boldsymbol{K}} \newcommand{\bmL}{\boldsymbol{L}} +\newcommand{\bmM}{\boldsymbol{M}} \newcommand{\bmN}{\boldsymbol{N}} +\newcommand{\bmO}{\boldsymbol{O}} \newcommand{\bmP}{\boldsymbol{P}} +\newcommand{\bmQ}{\boldsymbol{Q}} \newcommand{\bmR}{\boldsymbol{R}} +\newcommand{\bmS}{\boldsymbol{S}} \newcommand{\bmT}{\boldsymbol{T}} +\newcommand{\bmU}{\boldsymbol{U}} \newcommand{\bmV}{\boldsymbol{V}} +\newcommand{\bmW}{\boldsymbol{W}} \newcommand{\bmX}{\boldsymbol{X}} +\newcommand{\bmY}{\boldsymbol{Y}} \newcommand{\bmZ}{\boldsymbol{Z}} +%Small Letters +\newcommand{\bma}{\boldsymbol{a}} \newcommand{\bmb}{\boldsymbol{b}} +\newcommand{\bmc}{\boldsymbol{c}} \newcommand{\bmd}{\boldsymbol{d}} +\newcommand{\bme}{\boldsymbol{e}} \newcommand{\bmf}{\boldsymbol{f}} +\newcommand{\bmg}{\boldsymbol{g}} \newcommand{\bmh}{\boldsymbol{h}} +\newcommand{\bmi}{\boldsymbol{i}} \newcommand{\bmj}{\boldsymbol{j}} +\newcommand{\bmk}{\boldsymbol{k}} \newcommand{\bml}{\boldsymbol{l}} +\newcommand{\bmm}{\boldsymbol{m}} \newcommand{\bmn}{\boldsymbol{n}} +\newcommand{\bmo}{\boldsymbol{o}} \newcommand{\bmp}{\boldsymbol{p}} +\newcommand{\bmq}{\boldsymbol{q}} \newcommand{\bmr}{\boldsymbol{r}} +\newcommand{\bms}{\boldsymbol{s}} \newcommand{\bmt}{\boldsymbol{t}} +\newcommand{\bmu}{\boldsymbol{u}} \newcommand{\bmv}{\boldsymbol{v}} +\newcommand{\bmw}{\boldsymbol{w}} \newcommand{\bmx}{\boldsymbol{x}} +\newcommand{\bmy}{\boldsymbol{y}} \newcommand{\bmz}{\boldsymbol{z}} + +%--------------------------------------- +% Scr Math Fonts :- +%--------------------------------------- + +\newcommand{\sA}{{\mathscr{A}}} \newcommand{\sB}{{\mathscr{B}}} +\newcommand{\sC}{{\mathscr{C}}} \newcommand{\sD}{{\mathscr{D}}} +\newcommand{\sE}{{\mathscr{E}}} \newcommand{\sF}{{\mathscr{F}}} +\newcommand{\sG}{{\mathscr{G}}} \newcommand{\sH}{{\mathscr{H}}} +\newcommand{\sI}{{\mathscr{I}}} \newcommand{\sJ}{{\mathscr{J}}} +\newcommand{\sK}{{\mathscr{K}}} \newcommand{\sL}{{\mathscr{L}}} +\newcommand{\sM}{{\mathscr{M}}} \newcommand{\sN}{{\mathscr{N}}} +\newcommand{\sO}{{\mathscr{O}}} \newcommand{\sP}{{\mathscr{P}}} +\newcommand{\sQ}{{\mathscr{Q}}} \newcommand{\sR}{{\mathscr{R}}} +\newcommand{\sS}{{\mathscr{S}}} \newcommand{\sT}{{\mathscr{T}}} +\newcommand{\sU}{{\mathscr{U}}} \newcommand{\sV}{{\mathscr{V}}} +\newcommand{\sW}{{\mathscr{W}}} \newcommand{\sX}{{\mathscr{X}}} +\newcommand{\sY}{{\mathscr{Y}}} \newcommand{\sZ}{{\mathscr{Z}}} + + +%--------------------------------------- +% Math Fraktur Font +%--------------------------------------- + +%Captital Letters +\newcommand{\mfA}{\mathfrak{A}} \newcommand{\mfB}{\mathfrak{B}} +\newcommand{\mfC}{\mathfrak{C}} \newcommand{\mfD}{\mathfrak{D}} +\newcommand{\mfE}{\mathfrak{E}} \newcommand{\mfF}{\mathfrak{F}} +\newcommand{\mfG}{\mathfrak{G}} \newcommand{\mfH}{\mathfrak{H}} +\newcommand{\mfI}{\mathfrak{I}} \newcommand{\mfJ}{\mathfrak{J}} +\newcommand{\mfK}{\mathfrak{K}} \newcommand{\mfL}{\mathfrak{L}} +\newcommand{\mfM}{\mathfrak{M}} \newcommand{\mfN}{\mathfrak{N}} +\newcommand{\mfO}{\mathfrak{O}} \newcommand{\mfP}{\mathfrak{P}} +\newcommand{\mfQ}{\mathfrak{Q}} \newcommand{\mfR}{\mathfrak{R}} +\newcommand{\mfS}{\mathfrak{S}} \newcommand{\mfT}{\mathfrak{T}} +\newcommand{\mfU}{\mathfrak{U}} \newcommand{\mfV}{\mathfrak{V}} +\newcommand{\mfW}{\mathfrak{W}} \newcommand{\mfX}{\mathfrak{X}} +\newcommand{\mfY}{\mathfrak{Y}} \newcommand{\mfZ}{\mathfrak{Z}} +%Small Letters +\newcommand{\mfa}{\mathfrak{a}} \newcommand{\mfb}{\mathfrak{b}} +\newcommand{\mfc}{\mathfrak{c}} \newcommand{\mfd}{\mathfrak{d}} +\newcommand{\mfe}{\mathfrak{e}} \newcommand{\mff}{\mathfrak{f}} +\newcommand{\mfg}{\mathfrak{g}} \newcommand{\mfh}{\mathfrak{h}} +\newcommand{\mfi}{\mathfrak{i}} \newcommand{\mfj}{\mathfrak{j}} +\newcommand{\mfk}{\mathfrak{k}} \newcommand{\mfl}{\mathfrak{l}} +\newcommand{\mfm}{\mathfrak{m}} \newcommand{\mfn}{\mathfrak{n}} +\newcommand{\mfo}{\mathfrak{o}} \newcommand{\mfp}{\mathfrak{p}} +\newcommand{\mfq}{\mathfrak{q}} \newcommand{\mfr}{\mathfrak{r}} +\newcommand{\mfs}{\mathfrak{s}} \newcommand{\mft}{\mathfrak{t}} +\newcommand{\mfu}{\mathfrak{u}} \newcommand{\mfv}{\mathfrak{v}} +\newcommand{\mfw}{\mathfrak{w}} \newcommand{\mfx}{\mathfrak{x}} +\newcommand{\mfy}{\mathfrak{y}} \newcommand{\mfz}{\mathfrak{z}} diff --git a/6th-Semester-Spring-2024/Power-Electronics/Notes/macros.tex b/6th-Semester-Spring-2024/Power-Electronics/Notes/macros.tex new file mode 100644 index 0000000..8bbdb96 --- /dev/null +++ b/6th-Semester-Spring-2024/Power-Electronics/Notes/macros.tex @@ -0,0 +1,88 @@ +%From M275 "Topology" at SJSU +\newcommand{\id}{\mathrm{id}} +\newcommand{\taking}[1]{\xrightarrow{#1}} +\newcommand{\inv}{^{-1}} + +%From M170 "Introduction to Graph Theory" at SJSU +\DeclareMathOperator{\diam}{diam} +\DeclareMathOperator{\ord}{ord} +\newcommand{\defeq}{\overset{\mathrm{def}}{=}} + +%From the USAMO .tex files +\newcommand{\ts}{\textsuperscript} +\newcommand{\dg}{^\circ} +\newcommand{\ii}{\item} + +% % From Math 55 and Math 145 at Harvard +% \newenvironment{subproof}[1][Proof]{% +% \begin{proof}[#1] \renewcommand{\qedsymbol}{$\blacksquare$}}% +% {\end{proof}} + +\newcommand{\liff}{\leftrightarrow} +\newcommand{\lthen}{\rightarrow} +\newcommand{\opname}{\operatorname} +\newcommand{\surjto}{\twoheadrightarrow} +\newcommand{\injto}{\hookrightarrow} +\newcommand{\On}{\mathrm{On}} % ordinals +\DeclareMathOperator{\img}{im} % Image +\DeclareMathOperator{\Img}{Im} % Image 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b/6th-Semester-Spring-2024/Power-Electronics/Notes/power-electronics-notes.tex new file mode 100644 index 0000000..55ec08e --- /dev/null +++ b/6th-Semester-Spring-2024/Power-Electronics/Notes/power-electronics-notes.tex @@ -0,0 +1,119 @@ +\documentclass{report} + +\input{preamble} +\input{macros} +\input{letterfonts} +\usepackage{circuitikz} + +\title{\Huge{Power Electronics}} +\author{\huge{Aidan Sharpe}} +\date{} + +\begin{document} + +\maketitle +\newpage% or \cleardoublepage +% \pdfbookmark[<level>]{<title>}{<dest>} +\pdfbookmark[section]{\contentsname}{toc} +\tableofcontents +\pagebreak + +\chapter{} +\dfn{Power Electronics} +{ + Any electronics between the power source and the load. +} + +\dfn{Diode} +{ + A non-linear, polarized circuit component. Its positive terminal is called the anode, and its negative terminal is called the cathode. If the voltage at the anode is greater the voltage at the cathode, the diode will conduct. Otherwise, the diode behaves as an open circuit. +} + +An ideal diode, when conducting, will have no voltage drop, so it will behave like a direct short. An ideal diode, when not conducting, will allow no current to flow, so it will behave like an open circuit. + +For any periodic signal, the average value is given by: +$$V_\text{avg} = {1\over T} \int\limits_0^T x(\omega t) dt$$ +Where: +\begin{itemize} + \item[$\omega$] is the angular frequency of the signal, $x(\omega t)$ + \item[$T$] is the period of the signal, $x(\omega t)$ +\end{itemize} + +Since a half-wave rectifier only allows current to flow for half of a period, the average voltage out is only a fraction of the input voltage. + +\section{Half-Wave Recifier with Resistive Load and Inductive Filter} +Since inductors act like a flywheel for current, when an inductor is placed in series with the half-wave rectifier, the voltage across the load and inductor is not always positive. Adding this inductor, however, allows current to flow through the load for more time during each period. With a properly selected inductance, positive current may be able to flow throught the load for the entire period. + +\section{Freewheeling with Resistive Load and Inductive Filter} +Simply by adding a second diode, the inductor will slowly dissipate into the resistor between the positive cycles. This slow dissipations is called \emph{freewheeling}. Increasing the size of the inductor will result in less ripple in the output voltage. + +\begin{center} +\begin{circuitikz}[american voltages] +\draw +(0,0) to [short] (1,0) to [empty diode, l=$D_1$] (3,0) (3,-2) to [empty diode, l=$D_2$] (3,0) +(3,0) to [short, american inductor, l=$L_1$, i=$i_L$] (6,0) +to [short, american resistor, l_=$R_1$, v^=$V_R$] (6,-2) +to [short] (0,-2) +(0,0) to [vsourcesin, v_=$V_s$] (0,-2); +\end{circuitikz} +\end{center} +\noindent +For the first half-cycle ($0 < \omega t < \pi$): +\\ +\noindent +$D_1$ is on, $D_2$ is off, and $i_L = i_R$. +$$V_s \sin(\omega t) = L {d i_L \over dt} + i_l R$$ +$$i_L(t) = {V_s \over Z}\sin(\omega t - \varphi) + Ae^{-Rt/L}$$ +For the second half-cyle ($\pi < \omega t < 2\pi$): +$$V_L + V_R = 0$$ +$$L {d i_L \over dt} + i_L R = 0$$ +$$i_L(t) = Be^{-R(\omega t - \pi)/\omega L}$$ +Since $i_L(\pi)$ must be the same for both the first and the second half-cycles, the two equations must be equal at $t=\pi$. +$$i_L(\pi)=B$$ +$$i_L(0^+)=A-{V_s \over Z^2} \omega L$$ + +\section{Full Bridge with Resistive Load and Inductive Filter} + +\begin{center} + \begin{circuitikz}[american voltages] + \draw + (0,0) to [short] (3,0) to [american inductor, l=$L_1$] (6,0) + (0,-4) to [empty diode] (0,-2) to [empty diode] (0,0) + (3,-4) to [empty diode] (3,-2) to [empty diode] (3,0) + (0,-2) to [vsourcesin] (3,-2) + (6,0) to [american resistor, l=$R_1$] (6,-4) + (0,-4) to [short] (6,-4); + \end{circuitikz} +\end{center} + +\section{Periodic Steady State} +The periodic steady state is when a system returns to the same steady state at the end of each cycle. + +\ex{Inductor PSS} +{ +$$v_L = L {di_L \over dt}$$ +$$\langle v_L \rangle = {1 \over T} \int\limits_0^T v_L dt = {1 \over T} \int\limits_0^T L {di_L \over dt} dt$$ +$$\langle v_L \rangle = {L \over T} \lt[i_L(T) - i_L(0)\rt] = 0$$ +} + +\ex{Capacitor PSS} +{ + $$i_C = C {dv_C \over dt}$$ + $$\langle i_C \rangle = {1 \over T} \int\limits_0^T i_C dt = {1\over T} \int\limits_0^T C {dv_C \over dt} dt$$ + $$\langle i_C \rangle = {C \over T} \lt[v_C(T) - v_C(0)\rt] = 0$$ +} + +\section{Trigonometric Fourier Series} +For any periodic signal with period, $f(t) = f(t + nT), n \in \mathbb{Z}$, where $T$ is the period, a trigonometric series can be constructed to create an identical signal: +$$f(t) = {a_0 \over 2} + \sum_{n=1}^\infty (a_n \cos(n\omega t) + b_b \sin(n \omega t))$$ +where $\omega = {2\pi \over T}$. The value of $a_0$ is twice the average value of the signal: +$$a_0 = {2 \over T} \int\limits_{t_0}^{t_0 + T} f(t) dt.$$ +Additionally, the value of $a_n$ and $b_n$ are given by: +$$a_n = {2 \over T} \int\limits_{t_0}{t_0 + T} f(t)\cos(n \omega t) dt$$ +$$b_n = {2\over T} \int\limits_{t_0}{t_0 + T} f(t)\sin(n \omega t) dt.$$ +The term, $a_0 \over 2$ is the \emph{DC offset} of the signal. While the values of $a_n$ and $b_n$ are defined, since the only difference between $\sin$ and $\cos$ is a phase shift, the expression for the trigonometric Fourier series can be rewritten as: +$$f(t) = A_0 + \sum_{n=1}^\infty A_n \cos(n \omega t + \varphi_n)$$ +where $A_n = \sqrt{a_n^2 + b_n^2}$ and $\varphi_n = -\arctan\lt({b_n \over a_n}\rt)$ + + +\end{document} diff --git a/6th-Semester-Spring-2024/Power-Electronics/Notes/power-electronics-notes.toc b/6th-Semester-Spring-2024/Power-Electronics/Notes/power-electronics-notes.toc new file mode 100644 index 0000000..046439b --- /dev/null +++ b/6th-Semester-Spring-2024/Power-Electronics/Notes/power-electronics-notes.toc @@ -0,0 +1,7 @@ +\contentsline {chapter}{\numberline {1}}{2}{chapter.1}% +\contentsline {section}{\numberline {1.1}Half-Wave Recifier with Resistive Load and Inductive Filter}{2}{section.1.1}% +\contentsline {section}{\numberline {1.2}Freewheeling with Resistive Load and Inductive Filter}{2}{section.1.2}% +\contentsline {section}{\numberline {1.3}Full Bridge with Resistive Load and Inductive Filter}{3}{section.1.3}% +\contentsline {section}{\numberline {1.4}Periodic Steady State}{3}{section.1.4}% +\contentsline {section}{\numberline {1.5}Trigonometric Fourier Series}{4}{section.1.5}% +\contentsfinish diff --git a/6th-Semester-Spring-2024/Power-Electronics/Notes/preamble.tex b/6th-Semester-Spring-2024/Power-Electronics/Notes/preamble.tex new file mode 100644 index 0000000..af7d68e --- /dev/null +++ b/6th-Semester-Spring-2024/Power-Electronics/Notes/preamble.tex @@ -0,0 +1,779 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PACKAGE IMPORTS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\usepackage[tmargin=2cm,rmargin=1in,lmargin=1in,margin=0.85in,bmargin=2cm,footskip=.2in]{geometry} +\usepackage{amsmath,amsfonts,amsthm,amssymb,mathtools} +\usepackage{listings} +\usepackage[varbb]{newpxmath} +\usepackage{xfrac} +\usepackage[makeroom]{cancel} +\usepackage{mathtools} +\usepackage{bookmark} +\usepackage{enumitem} +\usepackage{hyperref,theoremref} +\hypersetup{ + pdftitle={Assignment}, + colorlinks=true, linkcolor=doc!90, + bookmarksnumbered=true, + bookmarksopen=true +} +\usepackage[most,many,breakable]{tcolorbox} +\usepackage{xcolor} +\usepackage{varwidth} +\usepackage{varwidth} +\usepackage{etoolbox} +%\usepackage{authblk} +\usepackage{nameref} +\usepackage{multicol,array} +\usepackage{tikz-cd} +\usepackage[ruled,vlined,linesnumbered]{algorithm2e} +\usepackage{comment} % enables the use of multi-line comments (\ifx \fi) +\usepackage{import} +\usepackage{xifthen} +\usepackage{pdfpages} +\usepackage{transparent} + +\newcommand\mycommfont[1]{\footnotesize\ttfamily\textcolor{blue}{#1}} +\SetCommentSty{mycommfont} +\newcommand{\incfig}[1]{% + \def\svgwidth{\columnwidth} + \import{./figures/}{#1.pdf_tex} +} + +\usepackage{tikzsymbols} +\renewcommand\qedsymbol{$\Laughey$} + + +%\usepackage{import} +%\usepackage{xifthen} +%\usepackage{pdfpages} +%\usepackage{transparent} + + 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\path[fill=tcbcolframe] (title.south west)--(title.south east) + to[out=0, in=180] ([xshift=5mm]title.east)-- + (title.center-|frame.east) + [rounded corners=\kvtcb@arc] |- + (frame.north) -| cycle; + }, +} +\makeatother + +%================================ +% Question BOX +%================================ + +\makeatletter +\newtcbtheorem{qstion}{Question}{enhanced, + breakable, + colback=white, + colframe=mygr, + attach boxed title to top left={yshift*=-\tcboxedtitleheight}, + fonttitle=\bfseries, + title={#2}, + boxed title size=title, + boxed title style={% + sharp corners, + rounded corners=northwest, + colback=tcbcolframe, + boxrule=0pt, + }, + underlay boxed title={% + \path[fill=tcbcolframe] (title.south west)--(title.south east) + to[out=0, in=180] ([xshift=5mm]title.east)-- + (title.center-|frame.east) + [rounded corners=\kvtcb@arc] |- + (frame.north) -| cycle; + }, + #1 +}{def} +\makeatother + +\newtcbtheorem[number within=chapter]{wconc}{Wrong Concept}{ + breakable, + enhanced, + colback=white, + colframe=myr, + arc=0pt, + outer arc=0pt, + fonttitle=\bfseries\sffamily\large, + colbacktitle=myr, + attach boxed title to top left={}, + boxed title style={ + enhanced, + skin=enhancedfirst jigsaw, + arc=3pt, + bottom=0pt, + interior style={fill=myr} + }, + #1 +}{def} + + + +%================================ +% NOTE BOX +%================================ + +\usetikzlibrary{arrows,calc,shadows.blur} +\tcbuselibrary{skins} +\newtcolorbox{note}[1][]{% + enhanced jigsaw, + colback=gray!20!white,% + colframe=gray!80!black, + size=small, + boxrule=1pt, + title=\textbf{Note:}, + halign title=flush center, + coltitle=black, + breakable, + drop shadow=black!50!white, + attach boxed title to top left={xshift=1cm,yshift=-\tcboxedtitleheight/2,yshifttext=-\tcboxedtitleheight/2}, + minipage boxed title=1.5cm, + boxed title style={% + colback=white, + size=fbox, + boxrule=1pt, + boxsep=2pt, + underlay={% + \coordinate (dotA) at ($(interior.west) + (-0.5pt,0)$); + \coordinate (dotB) at ($(interior.east) + (0.5pt,0)$); + \begin{scope} + \clip (interior.north west) rectangle ([xshift=3ex]interior.east); + \filldraw [white, blur shadow={shadow opacity=60, shadow yshift=-.75ex}, rounded corners=2pt] (interior.north west) rectangle (interior.south east); + \end{scope} + \begin{scope}[gray!80!black] + \fill (dotA) circle (2pt); + \fill (dotB) circle (2pt); + \end{scope} + }, + }, + #1, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% SELF MADE COMMANDS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\newcommand{\thm}[2]{\begin{Theorem}{#1}{}#2\end{Theorem}} +\newcommand{\cor}[2]{\begin{Corollary}{#1}{}#2\end{Corollary}} +\newcommand{\rvw}[2]{\begin{Review}{#1}{}#2\end{Review}} +\newcommand{\mthd}[2]{\begin{Method}{#1}{}#2\end{Method}} +\newcommand{\clm}[3]{\begin{claim}{#1}{#2}#3\end{claim}} +\newcommand{\wc}[2]{\begin{wconc}{#1}{}\setlength{\parindent}{1cm}#2\end{wconc}} +\newcommand{\thmcon}[1]{\begin{Theoremcon}{#1}\end{Theoremcon}} +\newcommand{\ex}[2]{\begin{Example}{#1}{}#2\end{Example}} +\newcommand{\dfn}[2]{\begin{Definition}[colbacktitle=red!75!black]{#1}{}#2\end{Definition}} +\newcommand{\dfnc}[2]{\begin{definition}[colbacktitle=red!75!black]{#1}{}#2\end{definition}} +\newcommand{\qs}[2]{\begin{question}{#1}{}#2\end{question}} +\newcommand{\pf}[2]{\begin{myproof}[#1]#2\end{myproof}} +\newcommand{\nt}[1]{\begin{note}#1\end{note}} + +\newcommand*\circled[1]{\tikz[baseline=(char.base)]{ + \node[shape=circle,draw,inner sep=1pt] (char) {#1};}} +\newcommand\getcurrentref[1]{% + \ifnumequal{\value{#1}}{0} + {??} + {\the\value{#1}}% +} +\newcommand{\getCurrentSectionNumber}{\getcurrentref{section}} +\newenvironment{myproof}[1][\proofname]{% + \proof[\bfseries #1: ]% +}{\endproof} + +\newcommand{\mclm}[2]{\begin{myclaim}[#1]#2\end{myclaim}} +\newenvironment{myclaim}[1][\claimname]{\proof[\bfseries #1: ]}{} + +\newcounter{mylabelcounter} + +\makeatletter +\newcommand{\setword}[2]{% + \phantomsection + #1\def\@currentlabel{\unexpanded{#1}}\label{#2}% +} +\makeatother + + + + +\tikzset{ + symbol/.style={ + draw=none, + every to/.append style={ + edge node={node [sloped, allow upside down, auto=false]{$#1$}}} + } +} + + +% deliminators +\DeclarePairedDelimiter{\abs}{\lvert}{\rvert} +\DeclarePairedDelimiter{\norm}{\lVert}{\rVert} + +\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil} +\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor} +\DeclarePairedDelimiter{\round}{\lfloor}{\rceil} + +\newsavebox\diffdbox +\newcommand{\slantedromand}{{\mathpalette\makesl{d}}} +\newcommand{\makesl}[2]{% +\begingroup +\sbox{\diffdbox}{$\mathsurround=0pt#1\mathrm{#2}$}% +\pdfsave +\pdfsetmatrix{1 0 0.2 1}% +\rlap{\usebox{\diffdbox}}% +\pdfrestore +\hskip\wd\diffdbox +\endgroup +} +\newcommand{\dd}[1][]{\ensuremath{\mathop{}\!\ifstrempty{#1}{% +\slantedromand\@ifnextchar^{\hspace{0.2ex}}{\hspace{0.1ex}}}% +{\slantedromand\hspace{0.2ex}^{#1}}}} +\ProvideDocumentCommand\dv{o m g}{% + \ensuremath{% + \IfValueTF{#3}{% + \IfNoValueTF{#1}{% + \frac{\dd #2}{\dd #3}% + }{% + \frac{\dd^{#1} #2}{\dd #3^{#1}}% + }% + }{% + \IfNoValueTF{#1}{% + \frac{\dd}{\dd #2}% + }{% + \frac{\dd^{#1}}{\dd #2^{#1}}% + }% + }% + }% +} +\providecommand*{\pdv}[3][]{\frac{\partial^{#1}#2}{\partial#3^{#1}}} +% - others +\DeclareMathOperator{\Lap}{\mathcal{L}} +\DeclareMathOperator{\Var}{Var} % varience +\DeclareMathOperator{\Cov}{Cov} % covarience +\DeclareMathOperator{\E}{E} % expected + +% Since the amsthm package isn't loaded + +% I prefer the slanted \leq +\let\oldleq\leq % save them in case they're every wanted +\let\oldgeq\geq +\renewcommand{\leq}{\leqslant} +\renewcommand{\geq}{\geqslant} + +% % redefine matrix env to allow for alignment, use r as default +% \renewcommand*\env@matrix[1][r]{\hskip -\arraycolsep +% \let\@ifnextchar\new@ifnextchar +% \array{*\c@MaxMatrixCols #1}} + + +%\usepackage{framed} +%\usepackage{titletoc} +%\usepackage{etoolbox} +%\usepackage{lmodern} + + +%\patchcmd{\tableofcontents}{\contentsname}{\sffamily\contentsname}{}{} + +%\renewenvironment{leftbar} +%{\def\FrameCommand{\hspace{6em}% +% {\color{myyellow}\vrule width 2pt depth 6pt}\hspace{1em}}% +% \MakeFramed{\parshape 1 0cm \dimexpr\textwidth-6em\relax\FrameRestore}\vskip2pt% +%} +%{\endMakeFramed} + +%\titlecontents{chapter} +%[0em]{\vspace*{2\baselineskip}} +%{\parbox{4.5em}{% +% \hfill\Huge\sffamily\bfseries\color{myred}\thecontentspage}% +% \vspace*{-2.3\baselineskip}\leftbar\textsc{\small\chaptername~\thecontentslabel}\\\sffamily} +%{}{\endleftbar} +%\titlecontents{section} +%[8.4em] +%{\sffamily\contentslabel{3em}}{}{} +%{\hspace{0.5em}\nobreak\itshape\color{myred}\contentspage} +%\titlecontents{subsection} +%[8.4em] +%{\sffamily\contentslabel{3em}}{}{} +%{\hspace{0.5em}\nobreak\itshape\color{myred}\contentspage} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% TABLE OF CONTENTS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\usepackage{tikz} +\definecolor{doc}{RGB}{0,60,110} +\usepackage{titletoc} +\contentsmargin{0cm} +\titlecontents{chapter}[3.7pc] +{\addvspace{30pt}% + \begin{tikzpicture}[remember picture, overlay]% + \draw[fill=doc!60,draw=doc!60] (-7,-.1) rectangle (-0.9,.5);% + \pgftext[left,x=-3.5cm,y=0.2cm]{\color{white}\Large\sc\bfseries Chapter\ \thecontentslabel};% + \end{tikzpicture}\color{doc!60}\large\sc\bfseries}% +{} +{} +{\;\titlerule\;\large\sc\bfseries Page \thecontentspage + \begin{tikzpicture}[remember picture, overlay] + \draw[fill=doc!60,draw=doc!60] (2pt,0) rectangle (4,0.1pt); + \end{tikzpicture}}% +\titlecontents{section}[3.7pc] +{\addvspace{2pt}} +{\contentslabel[\thecontentslabel]{2pc}} +{} +{\hfill\small \thecontentspage} +[] +\titlecontents*{subsection}[3.7pc] +{\addvspace{-1pt}\small} +{} +{} +{\ --- \small\thecontentspage} +[ \textbullet\ ][] + +\makeatletter +\renewcommand{\tableofcontents}{% + \chapter*{% + \vspace*{-20\p@}% + \begin{tikzpicture}[remember picture, overlay]% + \pgftext[right,x=15cm,y=0.2cm]{\color{doc!60}\Huge\sc\bfseries \contentsname};% + \draw[fill=doc!60,draw=doc!60] (13,-.75) rectangle (20,1);% + \clip (13,-.75) rectangle (20,1); + \pgftext[right,x=15cm,y=0.2cm]{\color{white}\Huge\sc\bfseries \contentsname};% + \end{tikzpicture}}% + \@starttoc{toc}} +\makeatother + diff --git a/6th-Semester-Spring-2024/Power-Electronics/Simulations/Rectifier_Half_LR_withFreewheelingD.cir b/6th-Semester-Spring-2024/Power-Electronics/Simulations/Rectifier_Half_LR_withFreewheelingD.cir new file mode 100644 index 0000000..5120085 --- /dev/null +++ b/6th-Semester-Spring-2024/Power-Electronics/Simulations/Rectifier_Half_LR_withFreewheelingD.cir @@ -0,0 +1,36 @@ +*--- SIMULATE FILE + +*---SIMULATION PARAMETERS +.PARAM: ++ FS=60 ;SYSTEM SWITCHING FREQUENCY ++ TS={1/FS} ++ W={2*PI*FS} ++ CYCLE=3 ;SIMULATED CYCLES ++ START={500*TS} ++ END={START+CYCLE*TS} ++ STEP={TS/1000} + +.TRAN {STEP} {END} {START} {STEP} UIC + +*---CIRCUIT PARAMETERS +.PARAM: ++ VS = 110*SQRT(2) ++ L = 20M ++ R = 10 + +*.STEP PARAM L LIST 0.01M 25M 50M 100M + +*--- AC POWER SUPPLY +VIN IN 0 SINE(0 {VS} {FS} 0 0 0) + +*--- CIRCUIT DISCRIPTION +D1 IN D1OUT MYDIODE +D2 0 D1OUT MYDIODE +L D1OUT LOUT {L} IC=0 +R LOUT 0 {R} + +*--- MEASURE POWER AND EFFICIENCY +.MEAS TRAN VD AVG V(D1OUT) +.MEAS TRAN VR AVG V(LOUT) + +.MODEL MYDIODE D(RON=0.1M ROFF=100MEG VFWD=0.1M) diff --git a/6th-Semester-Spring-2024/Power-Electronics/Textbook/Textbook_Chapter1.pdf b/6th-Semester-Spring-2024/Power-Electronics/Textbook/Textbook_Chapter1.pdf new file mode 100644 index 0000000..9ac2cf3 Binary files /dev/null and b/6th-Semester-Spring-2024/Power-Electronics/Textbook/Textbook_Chapter1.pdf differ diff --git a/6th-Semester-Spring-2024/SysCon/Homework/Homework-1/Homework-1.aux b/6th-Semester-Spring-2024/SysCon/Homework/Homework-1/Homework-1.aux new file mode 100644 index 0000000..cda1505 --- /dev/null +++ b/6th-Semester-Spring-2024/SysCon/Homework/Homework-1/Homework-1.aux @@ -0,0 +1,3 @@ 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0000000..a5c66cf --- /dev/null +++ b/6th-Semester-Spring-2024/SysCon/Notes/SysCon-Notes.tex @@ -0,0 +1,330 @@ +\documentclass{report} + +\input{preamble} +\input{macros} +\input{letterfonts} + +\title{\Huge{Systems and Control}} +\author{\huge{Aidan Sharpe}} +\date{} + +\begin{document} + +\maketitle +\newpage% or \cleardoublepage +% \pdfbookmark[<level>]{<title>}{<dest>} +\pdfbookmark[section]{\contentsname}{toc} +\tableofcontents +\pagebreak + +\chapter{Control Systems: Introduction, Applications, Definitions} +$$\text{Input} \to \boxed{\text{System}} \to \text{Output}$$ + +To a system to a desired state, compare the current state with the objective, pass the difference to a controller, and pass the output of the controller back to the system. + +\section{Basic Definitions \& Lingo} + +\dfn{System Modelling} +{ + A mathematical or input/output description of the behavior of a system. +} + +\dfn{Control} +{ + The use of information to affect the operation of a device, machine, or system of any kind. +} + +Feedback is important to ensure that the objectives of the system are met. + +\dfn{Plant} +{ + The physical objective to control, impact or influence. +} + +\dfn{Control Objective} +{ + The desired behavior of a system. +} + +\dfn{Input} +{ + The signals used to control a plant. +} + +\dfn{Output} +{ + The measurements, data, and what is being sensed. +} + +\dfn{Process} +{ + The internal behavior of the plant as a result of the inputs. +} + +\dfn{Model} +{ + A mathematical description of the physics of the system. +} +Modelling is a useful tool for the engineering of a system. It can help to determine desired inputs, outputs, and processes. + +\dfn{Disturbances} +{ + Anything preventing the plant from achieving the desired output. +} +Every system will have external disturbances to deal with. The real world is never the same as the ideal world. + +\ex{Traffic Control} +{ + \textbf{Plant}: The transportation network---movement of cars, roads, connectivity, highways, physics of the network. + + \textbf{Processes}: the movement of cars, switching of traffic lights + + \textbf{Control Objective}: minimizing traffic + + \textbf{Input}: The changing of the traffic light signals + + \textbf{Output}: The movement of the cars + + \textbf{Disturbances}: Accidents, snow, bad drivers +} + +\section{Control Strategies} +Two common control strategies are the black box strategy and the model-based strategy. + +\dfn{Black Box Strategy} +{ +If the processes of a system are unknown, we can learn about the system by applying inputs and taking note of the outputs. While analysis is not possible on black box systems, there is no need for physical knowledge of the system. +} + +\dfn{Model-Based Strategy} +{ + Model-based strategies use mathematical models to describe the behavior of a system. Compared to the black box strategy, more knowledge of the system is required, but having this knowledge makes deeper analysis possible. +} + +Using a model-based strategy, two control methods can be applied: the open loop method and the closed-loop method. The open loop method has no feedback mechanism, and is therefore susceptible to disturbances; however, open loop control systems are much simpler to build and model. On the other hand, closed loop systems have a feedback mechanism to reduce the impacts of disturbances. This mechanism adds complexity to the system, which makes modelling more difficult. + +\chapter{Laplace Transforms, Transfer Functions, \& ODEs} + +\section{Laplace Transforms} +The Laplace transform is a mathematical tool used to take a function of time, $t$, and transform it into a function of the complex frequency variable, $s$. The one-sided Laplace tranform is of the form: + +$$F(s) = \mathcal{L}\lt[f(t)\rt] = \int\limits_0^\infty f(t) e^{-st} dt$$ + +Unfortunately, for some values of $s$, this integral is undefined. + +\dfn{Abscissa of Absolute Convergence} +{ + The \emph{abscissa of absolute convergece} is the region in which there +} + +\dfn{Unit Impulse Function} +{ + The \emph{unit impulse function}, $\delta(t)$ is given by: + $$\delta(t) = \begin{cases} + 1 & t = 0 \\ + 0 & \text{elsewhere} + \end{cases}$$ + The unit impulse function has the Laplace transform: + $$\mathcal{L}\lt[\delta(t)\rt] = \int_0^\infty \delta(t)e^{-st} dt = 1$$ +} + +\dfn{Unit Step Function} +{ + The \emph{unit step function}, $u(t)$ is defined as: + $$u(t) = \begin{cases} + 1 & t \ge 0 \\ + 0 & t < 0 + \end{cases}$$ + The unit step function has the Laplace transform: + $$\mathcal{L}\lt[u(t)\rt] = {1\over s}$$ +} + +\dfn{Unit Ramp Function} +{ + The \emph{unit ramp function}, $v(t)$ is defined as: + $$v(t) = \begin{cases} + t & t \ge 0 \\ + 0 & t < 0 + \end{cases}$$ + + The unit ramp function has Laplace tranform: + $$\mathcal{L}\lt[v(t)\rt] = {1 \over s^2}$$ +} + +\ex{} +{ + \begin{enumerate} + \item Take the Laplace transform of $f(t) = 5 \forall t \ge 0$: + $$f(t) = 5u(t)$$ + $$F(s) = \mathcal{L}\lt[f(t)\rt] = {5 \over s}$$ + \item Take the Laplace transform of $f(t) = 2t \forall t \ge 0$: + $$f(t) = 5v(t)$$ + $$F(s) = \mathcal{L}\lt[f(t)\rt] = {2 \over s^2}$$ + \item Take the Laplace transform of $f(t) = e^{-at}$: + $$f(t) = e^{-at}u(t)$$ + \end{enumerate} +} + +\subsection{Linearity} +By definition, Laplace transforms are a linear mapping. +$$\mathcal{L}\lt[a_1 f_1(t) + a_2 f_2(t)\rt] = a_1 F_1(s) + a_2 F_2(s)$$ + +\pf{Linearity of Laplace Transforms} +{ + $$\mathcal{L}[a_1 f_1(t) + a_2 f_2(t)] = \int\limits_0^\infty \lt(a_1 f_1(t) + a_2 f_2(t)\rt) e^{-st} dt$$ + + By the distributive property of multiplication: + $$(a_1 f_1(t) + a_2 f_2(t))e^{-st} = a_1 f_1(t) e^{-st} + a_2 f_2(t) e^{-st}$$ +} + +\subsection{Differentiation} +Differentiation is easy with a Laplace transform: +$$\mathcal{L}\lt[f'(t)\rt] = sF(s) - f(0)$$ +Where: +\begin{itemize} + \item[$f(0)$] is the initial condition of the function $f(t)$ at $t=0$ +\end{itemize} + +\noindent +In general: +$$\mathcal{L}[f^{(n)}] = s^n F(s) - s^{n-1} f(0) - s^{n-2} f'(0) - \cdots - sf^{(n-2)}(0) - f^{(n-1)}(0)$$ + +\subsection{Final Value Theorem} +Consider $F(s) = {N(s) \over D(s)}$. The poles of $F(s)$ will occur at the roots of $D(s)$, and the zeros of $F(s)$ will occur at the roots of $N(s)$. + +\thm{Final Value Theorem} +{ + If all of the poles of $sF(s)$ occur only in the left half plane (LHP): + $$\lim_{t \to \infty} f(t) = \lim_{s \to 0} s F(s)$$ +} + +\ex{} +{ + With all zero initial conditions for $y(t)$ and $u(t)$, a system is goverend by this second order ODE: + $$y''(t) + 3y'(t) + 2y(t) = 2u'(t) + u(t)$$ + Using the final value theorem, find $\lim_{t \to \infty} y(t) \text{ if } u(t) = 1$ + \\ + \\ + Take the Laplace transforms: + $$\mcL[y''(t)] = s^2Y(s) - sy(0) - y'(0)$$ + $$\mcL[y'(t)] = sY(s) - y(0)$$ + $$\mcL[u'(t)] = sU(s) - u(0)$$ + + Plugging back in: + $$s^2Y(s) + 3sY(s) + 2Y(s) = 2sU(s) + U(s)$$ + + $${Y(s) \over U(s)} = {2s + 1 \over s^2 + 3s + 2}$$ + + Since $u(t)$ is the unit step, $U(s) = {1\over s}$ + + $$Y(s) = {1 \over s}\cdot{2s + 1 \over s^2 + 3s + 2}$$ + + By the final value theorem of $y(t)$: + $$\lim_{t \to \infty} y(t) = \lim_{s\to 0} sY(s) = \lim_{s\to0} {2s + 1 \over s^2 + 3s + 2} = {1\over2}$$ +} + +\subsection{Initial Value Theorem} +\thm{Initial Value Theorem} +{ + $$\lim{t \to 0^+} f(t) = \lim_{s\to\infty} sF(s)$$ + If and only if the limit exists. +} + +\subsection{Convolution} +$$f_1(t) * f_2(t) = \int$$ + +\section{Partial Fraction Expansion} +One way to compute the inverse Laplace transform is with partial fraction expansion. Given a transfer function, $Y(s)$, it can be broken down into the quotient of two simple transfer functions: +$$Y(s) = {N(s) \over D(s)} = {b_0 s^m + b_1 s^{m-1} + b_2 s^{m-2} + \cdots + b_m \over a_0 s^n + a_1 s^{n-1} + a_2 s^{n-2} + \cdots + a_0}$$ + +\ex{Partial Fraction Expansion: Distinct Roots} +{ + $$F(s) = {1 \over s^2 + 5s + 6}$$ + Factoring the denominator gives: + $$F(s) = {1 \over (s+3)(s+2)} = {c_1 \over s+3} + {c_2 \over s+2}$$ + Find values for $c_1$ and $c_2$: + $$c_1 = \lim_{s\to-3} F(s)(s+3) = \lim_{s\to-3}{1\over s+2} = -1$$ + $$c_2 = \lim_{s\to-2} F(s)(s+2) = \lim_{s\to-2}{1\over s+3} = 1$$ + Plugging back in for $F(s)$ gives: + $$F(s) = {-1 \over s+3} + {1 \over s+2}$$ +} + +\ex{Partial Fraction Expansion: Repeated Roots} +{ + $$F(s) = {1 \over (s+1)(s+2)^2}$$ + Since the denominator is a third degree polynomial, there will be three partial fractions. Importantly, for repeated roots, there is a term for each power of the root: + $$F(s) = {c_1 \over s+1} + {c_2 \over s+2} + {c_3 \over (s+2)^2}$$ + Find the values of the constants: + $$c_1 = \lim_{s\to-1} F(s) (s+1) = \lim_{s\to-1} {1 \over (s+2)^2} = 1$$ + $$c_3 = \lim_{s\to-2} F(s) (s+2)^2 \lim_{s\to-2} {1 \over s+1} = -1$$ + To solve for $c_2$, we must pick some random, preferably easy to work with, number to plug in for $s$: + $$F(0) = {1\over4} = {c_1 \over 1} + {c_2 \over 2} + {c_3 \over 3}$$ + $${1\over4} = 1 + {c_2 \over 2} + {-1 \over 4}$$ + $$c_2 = -1$$ + To complete the inverse Laplace transform, plug in the constants: + $$F(s) = {1 \over s+1} - {1 \over s+2} - {1 \over (s+2)^2}$$ + $$f(t) = \lt[e^{-t} - e^{-2t} + te^{-2t}\rt] u(t)$$ +} + +\ex{Partial Fraction Expansion: Imaginary Roots} +{ + $$F(s) = {1 \over s(s^2 + 2s + 2)}$$ + Convert to partial fractions: + $$F(s) = {c_1 \over s} + {As + B \over s^2 + 2s + 2}$$ + Solve for constants: + $$c_1 = \lim_{s\to0} F(s) = {1\over2}$$ + $${1\over s(s^2 + 2s + 2)} = {1 \over 2s} + {As + B \over s^2 + 2s + 2}$$ + $${1 \over s(s^2 + 2s + 2)} = {(s^2 + 2s + 2) + 2s(As + B) \over 2s(s^2 + 2s + 2)}$$ + $$2 = (s^2 + 2s + 2) + 2As^2 + 2Bs$$ + $$2 = (2A + 1)s^2 + 2s(B+1) + 2$$ + $$A = -{1\over2}$$ + $$B = -1$$ + $$F(s) = {1 \over 2s} + {-{1\over2}s - 1 \over s^2 + 2s + 2}$$ + +} + +\section{Solving ODEs Using Laplace Transforms} + +\ex{} +{ + $$\ddot{y}(t) - y(t) = t$$ + $$y(0) = \dot{y}(0) = 1$$ + $$\mcL[\ddot{y}(t)] = s^2y(s) - s\dot{y}(0) - y(0)$$ + $$\mcL[y(t)] = y(s)$$ + $$\mcL[t] = {1\over s^2}$$ + $$s^2y(s) - s - 1 - y(s) = {1\over s^2}$$ + $$y(s)[s^2 - 1] = s + 1 + {1\over s^2}$$ + $$y(s)[s^2 -1] = {s^2(s+1) + 1 \over s^2}$$ + $$y(s) = {s^2(s+1) + 1 \over s^2(s^2 - 1)} = {1\over s-1} + {1 \over s^2(s^2 -1)} = {1\over s-1} + {c_1 \over s} + {c_2 \over s^2} + {c_3 \over s-1} + {c_4 \over s+1}$$ + +} + +\chapter{Modeling of Dynamical Systems} + +The transfer function of a system is written in the form: +$$F(s) = {Y(s) \over X(s)} = {b_m s^m + b_{m-1}s^{m-1} + \cdots + b_0 \over a_n s^n + b_{n-1} s^{n-1} + \cdots + a_0}$$ +The numerator of the system has order $m$, and the denominator has order $n$. We say that the order of the system is the same as the order of the denominator. The roots of the numerator are the zeros of the transfer function and are usually plotted with $\circ$. The roots of the denominator are the poles of the transfer function and are usually plotted as $\times$. +\\ +\\ +\noindent +The goal of using this transfer function is to find the output, $y(t)$, of the system. Using the definition of the transfer function, this is done quite easily: +$$F(s) = {Y(s) \over X(s)}$$ +$$Y(s) = X(s)F(s)$$ +$$y(t) = \mathcal{L}^{-1}\lt\{Y(s)\rt\} = \mathcal{L}^{-1}\lt\{X(s)F(s)\rt\}$$ +$$y(t) = x(t)f(t)$$ +If $x(t)$ is the unit step, $u(t)$, the output is called the step response, if $x(t)$ is the Dirac delta function, $\delta(t)$, the output is called the impulse response, and if $x(t)$ is the ramp function, $v(t)$, the output is called the velocity response. + +\chapter{Signal Flow Graphs} +Signal flow graphs are an alternative to block diagrams. They may consist of nodes, paths, gains, and loops. A node is a place on the diagram with a value defined as the sum of its inputs. Nodes may exist as inputs to the system, outputs from the system, or simply a measurable point in the system. Paths connect nodes together, showing the direction that a signal travels. Gains describe how a signal transforms when travelling along a path from one node to another. Loops are a series of at least one path that start and end at the same node. +\\ +\\ +\noindent +There exist some special types of paths and loops. A forward path connects the input directly to the output with no loops. A feedback path is just a loop, also called a feedback loop. A self-loop is a loop that connects a node back to itself without visiting any other nodes. +\\ +\\ +\noindent +Mason's Rule: +$$G(s) = {C(s) \over R(s)} = {\sum_k T_k \Delta_k \over \Delta}$$ +where $k$ is the number of forward paths, and $T_k$ is the gain of the $k^\text{th}$ forward-path, $\Delta$ is the determinant of the signal flow graph, and $\Delta_k$ is the associated path factor. +\end{document} + diff --git a/6th-Semester-Spring-2024/SysCon/Notes/SysCon-Notes.toc b/6th-Semester-Spring-2024/SysCon/Notes/SysCon-Notes.toc new file mode 100644 index 0000000..221e23d --- /dev/null +++ b/6th-Semester-Spring-2024/SysCon/Notes/SysCon-Notes.toc @@ -0,0 +1,15 @@ +\contentsline {chapter}{\numberline {1}Control Systems: Introduction, Applications, Definitions}{2}{chapter.1}% +\contentsline {section}{\numberline {1.1}Basic Definitions \& Lingo}{2}{section.1.1}% +\contentsline {section}{\numberline {1.2}Control Strategies}{3}{section.1.2}% +\contentsline {chapter}{\numberline {2}Laplace Transforms, Transfer Functions, \& ODEs}{4}{chapter.2}% +\contentsline {section}{\numberline {2.1}Laplace Transforms}{4}{section.2.1}% +\contentsline {subsection}{\numberline {2.1.1}Linearity}{5}{subsection.2.1.1}% +\contentsline {subsection}{\numberline {2.1.2}Differentiation}{5}{subsection.2.1.2}% +\contentsline {subsection}{\numberline {2.1.3}Final Value Theorem}{6}{subsection.2.1.3}% +\contentsline {subsection}{\numberline {2.1.4}Initial Value Theorem}{6}{subsection.2.1.4}% +\contentsline {subsection}{\numberline {2.1.5}Convolution}{6}{subsection.2.1.5}% +\contentsline {section}{\numberline {2.2}Partial Fraction Expansion}{7}{section.2.2}% +\contentsline {section}{\numberline {2.3}Solving ODEs Using Laplace Transforms}{8}{section.2.3}% +\contentsline {chapter}{\numberline {3}Modeling of Dynamical Systems}{9}{chapter.3}% +\contentsline {chapter}{\numberline {4}Signal Flow Graphs}{10}{chapter.4}% +\contentsfinish diff --git a/6th-Semester-Spring-2024/SysCon/Notes/letterfonts.tex b/6th-Semester-Spring-2024/SysCon/Notes/letterfonts.tex new file mode 100644 index 0000000..e28675f --- /dev/null +++ b/6th-Semester-Spring-2024/SysCon/Notes/letterfonts.tex @@ -0,0 +1,178 @@ +% Things Lie +\newcommand{\kb}{\mathfrak b} +\newcommand{\kg}{\mathfrak g} +\newcommand{\kh}{\mathfrak h} +\newcommand{\kn}{\mathfrak n} +\newcommand{\ku}{\mathfrak u} +\newcommand{\kz}{\mathfrak z} +\DeclareMathOperator{\Ext}{Ext} % Ext functor +\DeclareMathOperator{\Tor}{Tor} % Tor functor +\newcommand{\gl}{\opname{\mathfrak{gl}}} % frak gl group +\renewcommand{\sl}{\opname{\mathfrak{sl}}} % frak sl group chktex 6 + +% More script letters etc. +\newcommand{\SA}{\mathcal A} +\newcommand{\SB}{\mathcal B} +\newcommand{\SC}{\mathcal C} +\newcommand{\SF}{\mathcal F} +\newcommand{\SG}{\mathcal G} +\newcommand{\SH}{\mathcal H} +\newcommand{\OO}{\mathcal O} + +\newcommand{\SCA}{\mathscr A} +\newcommand{\SCB}{\mathscr B} +\newcommand{\SCC}{\mathscr C} +\newcommand{\SCD}{\mathscr D} +\newcommand{\SCE}{\mathscr E} +\newcommand{\SCF}{\mathscr F} +\newcommand{\SCG}{\mathscr G} +\newcommand{\SCH}{\mathscr H} + +% Mathfrak primes +\newcommand{\km}{\mathfrak m} +\newcommand{\kp}{\mathfrak p} +\newcommand{\kq}{\mathfrak q} + +% number sets +\newcommand{\RR}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{R}}{\mathbb{R}^{#1}}}} +\newcommand{\NN}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{N}}{\mathbb{N}^{#1}}}} +\newcommand{\ZZ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Z}}{\mathbb{Z}^{#1}}}} +\newcommand{\QQ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Q}}{\mathbb{Q}^{#1}}}} +\newcommand{\CC}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{C}}{\mathbb{C}^{#1}}}} +\newcommand{\PP}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{P}}{\mathbb{P}^{#1}}}} +\newcommand{\HH}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{H}}{\mathbb{H}^{#1}}}} +\newcommand{\FF}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{F}}{\mathbb{F}^{#1}}}} +% expected value +\newcommand{\EE}{\ensuremath{\mathbb{E}}} +\newcommand{\charin}{\text{ char }} +\DeclareMathOperator{\sign}{sign} +\DeclareMathOperator{\Aut}{Aut} +\DeclareMathOperator{\Inn}{Inn} +\DeclareMathOperator{\Syl}{Syl} +\DeclareMathOperator{\Gal}{Gal} +\DeclareMathOperator{\GL}{GL} % General linear group +\DeclareMathOperator{\SL}{SL} % Special linear group + +%--------------------------------------- +% BlackBoard Math Fonts :- +%--------------------------------------- + +%Captital Letters +\newcommand{\bbA}{\mathbb{A}} \newcommand{\bbB}{\mathbb{B}} +\newcommand{\bbC}{\mathbb{C}} \newcommand{\bbD}{\mathbb{D}} +\newcommand{\bbE}{\mathbb{E}} \newcommand{\bbF}{\mathbb{F}} +\newcommand{\bbG}{\mathbb{G}} \newcommand{\bbH}{\mathbb{H}} +\newcommand{\bbI}{\mathbb{I}} \newcommand{\bbJ}{\mathbb{J}} +\newcommand{\bbK}{\mathbb{K}} \newcommand{\bbL}{\mathbb{L}} +\newcommand{\bbM}{\mathbb{M}} \newcommand{\bbN}{\mathbb{N}} +\newcommand{\bbO}{\mathbb{O}} \newcommand{\bbP}{\mathbb{P}} +\newcommand{\bbQ}{\mathbb{Q}} \newcommand{\bbR}{\mathbb{R}} +\newcommand{\bbS}{\mathbb{S}} \newcommand{\bbT}{\mathbb{T}} +\newcommand{\bbU}{\mathbb{U}} \newcommand{\bbV}{\mathbb{V}} +\newcommand{\bbW}{\mathbb{W}} \newcommand{\bbX}{\mathbb{X}} +\newcommand{\bbY}{\mathbb{Y}} \newcommand{\bbZ}{\mathbb{Z}} + +%--------------------------------------- +% MathCal Fonts :- +%--------------------------------------- + +%Captital Letters +\newcommand{\mcA}{\mathcal{A}} \newcommand{\mcB}{\mathcal{B}} +\newcommand{\mcC}{\mathcal{C}} \newcommand{\mcD}{\mathcal{D}} +\newcommand{\mcE}{\mathcal{E}} \newcommand{\mcF}{\mathcal{F}} +\newcommand{\mcG}{\mathcal{G}} \newcommand{\mcH}{\mathcal{H}} +\newcommand{\mcI}{\mathcal{I}} \newcommand{\mcJ}{\mathcal{J}} +\newcommand{\mcK}{\mathcal{K}} \newcommand{\mcL}{\mathcal{L}} +\newcommand{\mcM}{\mathcal{M}} \newcommand{\mcN}{\mathcal{N}} +\newcommand{\mcO}{\mathcal{O}} \newcommand{\mcP}{\mathcal{P}} +\newcommand{\mcQ}{\mathcal{Q}} \newcommand{\mcR}{\mathcal{R}} +\newcommand{\mcS}{\mathcal{S}} \newcommand{\mcT}{\mathcal{T}} +\newcommand{\mcU}{\mathcal{U}} \newcommand{\mcV}{\mathcal{V}} +\newcommand{\mcW}{\mathcal{W}} \newcommand{\mcX}{\mathcal{X}} +\newcommand{\mcY}{\mathcal{Y}} \newcommand{\mcZ}{\mathcal{Z}} + + +%--------------------------------------- +% Bold Math Fonts :- +%--------------------------------------- + +%Captital Letters +\newcommand{\bmA}{\boldsymbol{A}} \newcommand{\bmB}{\boldsymbol{B}} +\newcommand{\bmC}{\boldsymbol{C}} \newcommand{\bmD}{\boldsymbol{D}} +\newcommand{\bmE}{\boldsymbol{E}} \newcommand{\bmF}{\boldsymbol{F}} +\newcommand{\bmG}{\boldsymbol{G}} \newcommand{\bmH}{\boldsymbol{H}} +\newcommand{\bmI}{\boldsymbol{I}} \newcommand{\bmJ}{\boldsymbol{J}} +\newcommand{\bmK}{\boldsymbol{K}} \newcommand{\bmL}{\boldsymbol{L}} +\newcommand{\bmM}{\boldsymbol{M}} \newcommand{\bmN}{\boldsymbol{N}} +\newcommand{\bmO}{\boldsymbol{O}} \newcommand{\bmP}{\boldsymbol{P}} +\newcommand{\bmQ}{\boldsymbol{Q}} \newcommand{\bmR}{\boldsymbol{R}} +\newcommand{\bmS}{\boldsymbol{S}} \newcommand{\bmT}{\boldsymbol{T}} +\newcommand{\bmU}{\boldsymbol{U}} \newcommand{\bmV}{\boldsymbol{V}} +\newcommand{\bmW}{\boldsymbol{W}} \newcommand{\bmX}{\boldsymbol{X}} +\newcommand{\bmY}{\boldsymbol{Y}} \newcommand{\bmZ}{\boldsymbol{Z}} +%Small Letters +\newcommand{\bma}{\boldsymbol{a}} \newcommand{\bmb}{\boldsymbol{b}} +\newcommand{\bmc}{\boldsymbol{c}} \newcommand{\bmd}{\boldsymbol{d}} +\newcommand{\bme}{\boldsymbol{e}} \newcommand{\bmf}{\boldsymbol{f}} +\newcommand{\bmg}{\boldsymbol{g}} \newcommand{\bmh}{\boldsymbol{h}} +\newcommand{\bmi}{\boldsymbol{i}} \newcommand{\bmj}{\boldsymbol{j}} +\newcommand{\bmk}{\boldsymbol{k}} \newcommand{\bml}{\boldsymbol{l}} +\newcommand{\bmm}{\boldsymbol{m}} \newcommand{\bmn}{\boldsymbol{n}} +\newcommand{\bmo}{\boldsymbol{o}} \newcommand{\bmp}{\boldsymbol{p}} +\newcommand{\bmq}{\boldsymbol{q}} \newcommand{\bmr}{\boldsymbol{r}} +\newcommand{\bms}{\boldsymbol{s}} \newcommand{\bmt}{\boldsymbol{t}} +\newcommand{\bmu}{\boldsymbol{u}} \newcommand{\bmv}{\boldsymbol{v}} +\newcommand{\bmw}{\boldsymbol{w}} \newcommand{\bmx}{\boldsymbol{x}} +\newcommand{\bmy}{\boldsymbol{y}} \newcommand{\bmz}{\boldsymbol{z}} + +%--------------------------------------- +% Scr Math Fonts :- +%--------------------------------------- + +\newcommand{\sA}{{\mathscr{A}}} \newcommand{\sB}{{\mathscr{B}}} +\newcommand{\sC}{{\mathscr{C}}} \newcommand{\sD}{{\mathscr{D}}} +\newcommand{\sE}{{\mathscr{E}}} \newcommand{\sF}{{\mathscr{F}}} +\newcommand{\sG}{{\mathscr{G}}} \newcommand{\sH}{{\mathscr{H}}} +\newcommand{\sI}{{\mathscr{I}}} \newcommand{\sJ}{{\mathscr{J}}} +\newcommand{\sK}{{\mathscr{K}}} \newcommand{\sL}{{\mathscr{L}}} +\newcommand{\sM}{{\mathscr{M}}} \newcommand{\sN}{{\mathscr{N}}} +\newcommand{\sO}{{\mathscr{O}}} \newcommand{\sP}{{\mathscr{P}}} +\newcommand{\sQ}{{\mathscr{Q}}} \newcommand{\sR}{{\mathscr{R}}} +\newcommand{\sS}{{\mathscr{S}}} \newcommand{\sT}{{\mathscr{T}}} +\newcommand{\sU}{{\mathscr{U}}} \newcommand{\sV}{{\mathscr{V}}} +\newcommand{\sW}{{\mathscr{W}}} \newcommand{\sX}{{\mathscr{X}}} +\newcommand{\sY}{{\mathscr{Y}}} \newcommand{\sZ}{{\mathscr{Z}}} + + +%--------------------------------------- +% Math Fraktur Font +%--------------------------------------- + +%Captital Letters +\newcommand{\mfA}{\mathfrak{A}} \newcommand{\mfB}{\mathfrak{B}} +\newcommand{\mfC}{\mathfrak{C}} \newcommand{\mfD}{\mathfrak{D}} +\newcommand{\mfE}{\mathfrak{E}} \newcommand{\mfF}{\mathfrak{F}} +\newcommand{\mfG}{\mathfrak{G}} \newcommand{\mfH}{\mathfrak{H}} +\newcommand{\mfI}{\mathfrak{I}} \newcommand{\mfJ}{\mathfrak{J}} +\newcommand{\mfK}{\mathfrak{K}} \newcommand{\mfL}{\mathfrak{L}} +\newcommand{\mfM}{\mathfrak{M}} \newcommand{\mfN}{\mathfrak{N}} +\newcommand{\mfO}{\mathfrak{O}} \newcommand{\mfP}{\mathfrak{P}} +\newcommand{\mfQ}{\mathfrak{Q}} \newcommand{\mfR}{\mathfrak{R}} +\newcommand{\mfS}{\mathfrak{S}} \newcommand{\mfT}{\mathfrak{T}} +\newcommand{\mfU}{\mathfrak{U}} \newcommand{\mfV}{\mathfrak{V}} +\newcommand{\mfW}{\mathfrak{W}} \newcommand{\mfX}{\mathfrak{X}} +\newcommand{\mfY}{\mathfrak{Y}} \newcommand{\mfZ}{\mathfrak{Z}} +%Small Letters +\newcommand{\mfa}{\mathfrak{a}} \newcommand{\mfb}{\mathfrak{b}} +\newcommand{\mfc}{\mathfrak{c}} \newcommand{\mfd}{\mathfrak{d}} +\newcommand{\mfe}{\mathfrak{e}} \newcommand{\mff}{\mathfrak{f}} +\newcommand{\mfg}{\mathfrak{g}} \newcommand{\mfh}{\mathfrak{h}} +\newcommand{\mfi}{\mathfrak{i}} \newcommand{\mfj}{\mathfrak{j}} +\newcommand{\mfk}{\mathfrak{k}} \newcommand{\mfl}{\mathfrak{l}} +\newcommand{\mfm}{\mathfrak{m}} \newcommand{\mfn}{\mathfrak{n}} +\newcommand{\mfo}{\mathfrak{o}} \newcommand{\mfp}{\mathfrak{p}} +\newcommand{\mfq}{\mathfrak{q}} \newcommand{\mfr}{\mathfrak{r}} +\newcommand{\mfs}{\mathfrak{s}} \newcommand{\mft}{\mathfrak{t}} +\newcommand{\mfu}{\mathfrak{u}} \newcommand{\mfv}{\mathfrak{v}} +\newcommand{\mfw}{\mathfrak{w}} \newcommand{\mfx}{\mathfrak{x}} +\newcommand{\mfy}{\mathfrak{y}} \newcommand{\mfz}{\mathfrak{z}} diff --git a/6th-Semester-Spring-2024/SysCon/Notes/macros.tex b/6th-Semester-Spring-2024/SysCon/Notes/macros.tex new file mode 100644 index 0000000..169a683 --- /dev/null +++ b/6th-Semester-Spring-2024/SysCon/Notes/macros.tex @@ -0,0 +1,90 @@ +%From M275 "Topology" at SJSU + +%Take the Laplace transfoms: +\newcommand{\id}{\mathrm{id}} +\newcommand{\taking}[1]{\xrightarrow{#1}} +\newcommand{\inv}{^{-1}} + +%From M170 "Introduction to Graph Theory" at SJSU +\DeclareMathOperator{\diam}{diam} +\DeclareMathOperator{\ord}{ord} +\newcommand{\defeq}{\overset{\mathrm{def}}{=}} + +%From the USAMO .tex files +\newcommand{\ts}{\textsuperscript} +\newcommand{\dg}{^\circ} +\newcommand{\ii}{\item} + +% % From Math 55 and Math 145 at Harvard +% \newenvironment{subproof}[1][Proof]{% +% \begin{proof}[#1] \renewcommand{\qedsymbol}{$\blacksquare$}}% +% {\end{proof}} + +\newcommand{\liff}{\leftrightarrow} +\newcommand{\lthen}{\rightarrow} +\newcommand{\opname}{\operatorname} +\newcommand{\surjto}{\twoheadrightarrow} +\newcommand{\injto}{\hookrightarrow} +\newcommand{\On}{\mathrm{On}} % ordinals +\DeclareMathOperator{\img}{im} % Image +\DeclareMathOperator{\Img}{Im} % Image +\DeclareMathOperator{\coker}{coker} % Cokernel +\DeclareMathOperator{\Coker}{Coker} % Cokernel +\DeclareMathOperator{\Ker}{Ker} % Kernel +\DeclareMathOperator{\rank}{rank} +\DeclareMathOperator{\Spec}{Spec} % spectrum +\DeclareMathOperator{\Tr}{Tr} % trace +\DeclareMathOperator{\pr}{pr} % projection +\DeclareMathOperator{\ext}{ext} % extension +\DeclareMathOperator{\pred}{pred} % predecessor +\DeclareMathOperator{\dom}{dom} % domain +\DeclareMathOperator{\ran}{ran} % range +\DeclareMathOperator{\Hom}{Hom} % homomorphism +\DeclareMathOperator{\Mor}{Mor} % morphisms +\DeclareMathOperator{\End}{End} % endomorphism + +\newcommand{\eps}{\epsilon} +\newcommand{\veps}{\varepsilon} +\newcommand{\ol}{\overline} +\newcommand{\ul}{\underline} +\newcommand{\wt}{\widetilde} +\newcommand{\wh}{\widehat} +\newcommand{\vocab}[1]{\textbf{\color{blue} #1}} +\providecommand{\half}{\frac{1}{2}} +\newcommand{\dang}{\measuredangle} %% Directed angle +\newcommand{\ray}[1]{\overrightarrow{#1}} +\newcommand{\seg}[1]{\overline{#1}} +\newcommand{\arc}[1]{\wideparen{#1}} +\DeclareMathOperator{\cis}{cis} +\DeclareMathOperator*{\lcm}{lcm} +\DeclareMathOperator*{\argmin}{arg min} +\DeclareMathOperator*{\argmax}{arg max} +\newcommand{\cycsum}{\sum_{\mathrm{cyc}}} +\newcommand{\symsum}{\sum_{\mathrm{sym}}} +\newcommand{\cycprod}{\prod_{\mathrm{cyc}}} +\newcommand{\symprod}{\prod_{\mathrm{sym}}} +\newcommand{\Qed}{\begin{flushright}\qed\end{flushright}} +\newcommand{\parinn}{\setlength{\parindent}{1cm}} +\newcommand{\parinf}{\setlength{\parindent}{0cm}} +% \newcommand{\norm}{\|\cdot\|} +\newcommand{\inorm}{\norm_{\infty}} +\newcommand{\opensets}{\{V_{\alpha}\}_{\alpha\in I}} +\newcommand{\oset}{V_{\alpha}} +\newcommand{\opset}[1]{V_{\alpha_{#1}}} +\newcommand{\lub}{\text{lub}} +\newcommand{\del}[2]{\frac{\partial #1}{\partial #2}} +\newcommand{\Del}[3]{\frac{\partial^{#1} #2}{\partial^{#1} #3}} +\newcommand{\deld}[2]{\dfrac{\partial #1}{\partial #2}} +\newcommand{\Deld}[3]{\dfrac{\partial^{#1} #2}{\partial^{#1} #3}} +\newcommand{\lm}{\lambda} +\newcommand{\uin}{\mathbin{\rotatebox[origin=c]{90}{$\in$}}} +\newcommand{\usubset}{\mathbin{\rotatebox[origin=c]{90}{$\subset$}}} +\newcommand{\lt}{\left} +\newcommand{\rt}{\right} +\newcommand{\bs}[1]{\boldsymbol{#1}} +\newcommand{\exs}{\exists} +\newcommand{\st}{\strut} +\newcommand{\dps}[1]{\displaystyle{#1}} + +\newcommand{\sol}{\setlength{\parindent}{0cm}\textbf{\textit{Solution:}}\setlength{\parindent}{1cm} } +\newcommand{\solve}[1]{\setlength{\parindent}{0cm}\textbf{\textit{Solution: }}\setlength{\parindent}{1cm}#1 \Qed} diff --git a/6th-Semester-Spring-2024/SysCon/Notes/preamble.tex b/6th-Semester-Spring-2024/SysCon/Notes/preamble.tex new file mode 100644 index 0000000..af7d68e --- /dev/null +++ b/6th-Semester-Spring-2024/SysCon/Notes/preamble.tex @@ -0,0 +1,779 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% PACKAGE IMPORTS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\usepackage[tmargin=2cm,rmargin=1in,lmargin=1in,margin=0.85in,bmargin=2cm,footskip=.2in]{geometry} +\usepackage{amsmath,amsfonts,amsthm,amssymb,mathtools} +\usepackage{listings} +\usepackage[varbb]{newpxmath} +\usepackage{xfrac} +\usepackage[makeroom]{cancel} +\usepackage{mathtools} +\usepackage{bookmark} +\usepackage{enumitem} +\usepackage{hyperref,theoremref} +\hypersetup{ + pdftitle={Assignment}, + colorlinks=true, linkcolor=doc!90, + bookmarksnumbered=true, + bookmarksopen=true +} +\usepackage[most,many,breakable]{tcolorbox} +\usepackage{xcolor} +\usepackage{varwidth} +\usepackage{varwidth} +\usepackage{etoolbox} +%\usepackage{authblk} +\usepackage{nameref} +\usepackage{multicol,array} +\usepackage{tikz-cd} +\usepackage[ruled,vlined,linesnumbered]{algorithm2e} +\usepackage{comment} % enables the use of multi-line comments (\ifx \fi) +\usepackage{import} +\usepackage{xifthen} +\usepackage{pdfpages} +\usepackage{transparent} + +\newcommand\mycommfont[1]{\footnotesize\ttfamily\textcolor{blue}{#1}} +\SetCommentSty{mycommfont} +\newcommand{\incfig}[1]{% + \def\svgwidth{\columnwidth} + \import{./figures/}{#1.pdf_tex} +} + +\usepackage{tikzsymbols} +\renewcommand\qedsymbol{$\Laughey$} + + +%\usepackage{import} +%\usepackage{xifthen} +%\usepackage{pdfpages} +%\usepackage{transparent} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% SELF MADE COLORS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +\definecolor{myg}{RGB}{56, 140, 70} +\definecolor{myb}{RGB}{45, 111, 177} +\definecolor{myr}{RGB}{199, 68, 64} +\definecolor{mytheorembg}{HTML}{F2F2F9} +\definecolor{mytheoremfr}{HTML}{00007B} +\definecolor{mylenmabg}{HTML}{FFFAF8} +\definecolor{mylenmafr}{HTML}{983b0f} +\definecolor{mypropbg}{HTML}{f2fbfc} +\definecolor{mypropfr}{HTML}{191971} +\definecolor{myexamplebg}{HTML}{F2FBF8} +\definecolor{myexamplefr}{HTML}{88D6D1} +\definecolor{myexampleti}{HTML}{2A7F7F} +\definecolor{mydefinitbg}{HTML}{E5E5FF} +\definecolor{mydefinitfr}{HTML}{3F3FA3} +\definecolor{notesgreen}{RGB}{0,162,0} +\definecolor{myp}{RGB}{197, 92, 212} +\definecolor{mygr}{HTML}{2C3338} +\definecolor{myred}{RGB}{127,0,0} +\definecolor{myyellow}{RGB}{169,121,69} +\definecolor{myexercisebg}{HTML}{F2FBF8} +\definecolor{myexercisefg}{HTML}{88D6D1} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% TCOLORBOX SETUPS +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\setlength{\parindent}{1cm} +%================================ +% THEOREM BOX +%================================ + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{Theorem}{Theorem} +{% + enhanced, + breakable, + colback = mytheorembg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{mytheoremfr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mytheoremfr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mytheoremfr}, +} +{th} + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=chapter]{theorem}{Theorem} +{% + enhanced, + breakable, + colback = mytheorembg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{mytheoremfr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mytheoremfr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mytheoremfr}, +} +{th} + + +\tcbuselibrary{theorems,skins,hooks} +\newtcolorbox{Theoremcon} +{% + enhanced + ,breakable + ,colback = mytheorembg + ,frame hidden + ,boxrule = 0sp + ,borderline west = {2pt}{0pt}{mytheoremfr} + ,sharp corners + ,description font = \mdseries + ,separator sign none +} + +%================================ +% Corollery +%================================ +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{Corollary}{Corollary} +{% + enhanced + ,breakable + ,colback = myp!10 + ,frame hidden + ,boxrule = 0sp + ,borderline west = {2pt}{0pt}{myp!85!black} + ,sharp corners + ,detach title + ,before upper = \tcbtitle\par\smallskip + ,coltitle = myp!85!black + ,fonttitle = \bfseries\sffamily + ,description font = \mdseries + ,separator sign none + ,segmentation style={solid, myp!85!black} +} +{th} +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=chapter]{corollary}{Corollary} +{% + enhanced + ,breakable + ,colback = myp!10 + ,frame hidden + ,boxrule = 0sp + ,borderline west = {2pt}{0pt}{myp!85!black} + ,sharp corners + ,detach title + ,before upper = \tcbtitle\par\smallskip + ,coltitle = myp!85!black + ,fonttitle = \bfseries\sffamily + ,description font = \mdseries + ,separator sign none + ,segmentation style={solid, myp!85!black} +} +{th} + + +%================================ +% LENMA +%================================ + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{Review}{Review} +{% + enhanced, + breakable, + colback = mylenmabg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{mylenmafr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mylenmafr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mylenmafr}, +} +{th} + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=chapter]{review}{Review} +{% + enhanced, + breakable, + colback = mylenmabg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{mylenmafr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mylenmafr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mylenmafr}, +} +{th} + + +%================================ +% METHOD +%================================ + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{Method}{Method} +{% + enhanced, + breakable, + colback = mypropbg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{mypropfr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mypropfr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mypropfr}, +} +{th} + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=chapter]{method}{Method} +{% + enhanced, + breakable, + colback = mypropbg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{mypropfr}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = mypropfr, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, mypropfr}, +} +{th} + + +%================================ +% CLAIM +%================================ + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{claim}{Claim} +{% + enhanced + ,breakable + ,colback = myg!10 + ,frame hidden + ,boxrule = 0sp + ,borderline west = {2pt}{0pt}{myg} + ,sharp corners + ,detach title + ,before upper = \tcbtitle\par\smallskip + ,coltitle = myg!85!black + ,fonttitle = \bfseries\sffamily + ,description font = \mdseries + ,separator sign none + ,segmentation style={solid, myg!85!black} +} +{th} + + + +%================================ +% Exercise +%================================ + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=section]{Exercise}{Exercise} +{% + enhanced, + breakable, + colback = myexercisebg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{myexercisefg}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = myexercisefg, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, myexercisefg}, +} +{th} + +\tcbuselibrary{theorems,skins,hooks} +\newtcbtheorem[number within=chapter]{exercise}{Exercise} +{% + enhanced, + breakable, + colback = myexercisebg, + frame hidden, + boxrule = 0sp, + borderline west = {2pt}{0pt}{myexercisefg}, + sharp corners, + detach title, + before upper = \tcbtitle\par\smallskip, + coltitle = myexercisefg, + fonttitle = \bfseries\sffamily, + description font = \mdseries, + separator sign none, + segmentation style={solid, myexercisefg}, +} +{th} + +%================================ +% EXAMPLE BOX +%================================ + +\newtcbtheorem[number within=section]{Example}{Example} +{% + colback = myexamplebg + ,breakable + ,colframe = myexamplefr + ,coltitle = myexampleti + ,boxrule = 1pt + ,sharp corners + ,detach title + ,before upper=\tcbtitle\par\smallskip + ,fonttitle = \bfseries + ,description font = \mdseries + ,separator sign none + ,description delimiters parenthesis +} +{ex} + +\newtcbtheorem[number within=chapter]{example}{Example} +{% + colback = myexamplebg + ,breakable + ,colframe = myexamplefr + ,coltitle = myexampleti + ,boxrule = 1pt + ,sharp corners + ,detach title + ,before upper=\tcbtitle\par\smallskip + ,fonttitle = \bfseries + ,description font = \mdseries + ,separator sign none + ,description delimiters parenthesis +} +{ex} + +%================================ +% DEFINITION BOX +%================================ + +\newtcbtheorem[number within=section]{Definition}{Definition}{enhanced, + before skip=2mm,after skip=2mm, colback=red!5,colframe=red!80!black,boxrule=0.5mm, + attach boxed title to top left={xshift=1cm,yshift*=1mm-\tcboxedtitleheight}, varwidth boxed title*=-3cm, + boxed title style={frame code={ + \path[fill=tcbcolback] + ([yshift=-1mm,xshift=-1mm]frame.north west) + arc[start angle=0,end angle=180,radius=1mm] + ([yshift=-1mm,xshift=1mm]frame.north east) + arc[start angle=180,end angle=0,radius=1mm]; + \path[left color=tcbcolback!60!black,right color=tcbcolback!60!black, + middle color=tcbcolback!80!black] + ([xshift=-2mm]frame.north west) -- ([xshift=2mm]frame.north east) + [rounded corners=1mm]-- ([xshift=1mm,yshift=-1mm]frame.north east) + -- (frame.south east) -- (frame.south west) + -- ([xshift=-1mm,yshift=-1mm]frame.north west) + [sharp corners]-- cycle; + },interior engine=empty, + }, + fonttitle=\bfseries, + title={#2},#1}{def} +\newtcbtheorem[number within=chapter]{definition}{Definition}{enhanced, + before skip=2mm,after skip=2mm, colback=red!5,colframe=red!80!black,boxrule=0.5mm, + attach boxed title to top left={xshift=1cm,yshift*=1mm-\tcboxedtitleheight}, varwidth boxed title*=-3cm, + boxed title style={frame code={ + \path[fill=tcbcolback] + ([yshift=-1mm,xshift=-1mm]frame.north west) + arc[start angle=0,end angle=180,radius=1mm] + ([yshift=-1mm,xshift=1mm]frame.north east) + arc[start angle=180,end angle=0,radius=1mm]; + \path[left color=tcbcolback!60!black,right color=tcbcolback!60!black, + middle color=tcbcolback!80!black] + ([xshift=-2mm]frame.north west) -- ([xshift=2mm]frame.north east) + [rounded corners=1mm]-- ([xshift=1mm,yshift=-1mm]frame.north east) + -- (frame.south east) -- (frame.south west) + -- ([xshift=-1mm,yshift=-1mm]frame.north west) + [sharp corners]-- cycle; + },interior engine=empty, + }, + fonttitle=\bfseries, + title={#2},#1}{def} + + + +%================================ +% Solution BOX +%================================ + +\makeatletter +\newtcbtheorem{question}{Question}{enhanced, + breakable, + colback=white, + colframe=myb!80!black, + attach boxed title to top left={yshift*=-\tcboxedtitleheight}, + fonttitle=\bfseries, + title={#2}, + boxed title size=title, + boxed title style={% + sharp corners, + rounded corners=northwest, + colback=tcbcolframe, + boxrule=0pt, + }, + underlay boxed title={% + \path[fill=tcbcolframe] (title.south west)--(title.south east) + to[out=0, in=180] ([xshift=5mm]title.east)-- + (title.center-|frame.east) + [rounded corners=\kvtcb@arc] |- + (frame.north) -| cycle; + }, + #1 +}{def} +\makeatother + +%================================ +% SOLUTION BOX +%================================ + +\makeatletter +\newtcolorbox{solution}{enhanced, + breakable, + colback=white, + colframe=myg!80!black, + attach boxed title to top left={yshift*=-\tcboxedtitleheight}, + title=Solution, + boxed title size=title, + boxed title style={% + sharp corners, + rounded corners=northwest, + colback=tcbcolframe, + boxrule=0pt, + }, + underlay boxed title={% + \path[fill=tcbcolframe] (title.south west)--(title.south east) + to[out=0, in=180] ([xshift=5mm]title.east)-- + (title.center-|frame.east) + [rounded corners=\kvtcb@arc] |- + (frame.north) -| cycle; + }, +} +\makeatother + +%================================ +% Question BOX +%================================ + +\makeatletter +\newtcbtheorem{qstion}{Question}{enhanced, + breakable, + colback=white, + colframe=mygr, + attach boxed title to top left={yshift*=-\tcboxedtitleheight}, + fonttitle=\bfseries, + title={#2}, + boxed title size=title, + boxed title style={% + sharp corners, + rounded corners=northwest, + colback=tcbcolframe, + boxrule=0pt, + }, + underlay boxed title={% + \path[fill=tcbcolframe] (title.south west)--(title.south east) + to[out=0, in=180] ([xshift=5mm]title.east)-- + (title.center-|frame.east) + [rounded corners=\kvtcb@arc] |- + (frame.north) -| cycle; + }, + #1 +}{def} +\makeatother + +\newtcbtheorem[number within=chapter]{wconc}{Wrong Concept}{ + breakable, + enhanced, + colback=white, + colframe=myr, + arc=0pt, + outer arc=0pt, + fonttitle=\bfseries\sffamily\large, + colbacktitle=myr, + attach boxed title to top left={}, + boxed title style={ + enhanced, + skin=enhancedfirst jigsaw, + arc=3pt, + bottom=0pt, + interior style={fill=myr} + }, + #1 +}{def} + + + +%================================ +% NOTE BOX +%================================ + +\usetikzlibrary{arrows,calc,shadows.blur} +\tcbuselibrary{skins} +\newtcolorbox{note}[1][]{% + enhanced jigsaw, + colback=gray!20!white,% + colframe=gray!80!black, + size=small, + boxrule=1pt, + title=\textbf{Note:}, + halign title=flush center, + coltitle=black, + breakable, + drop shadow=black!50!white, + attach boxed title to top left={xshift=1cm,yshift=-\tcboxedtitleheight/2,yshifttext=-\tcboxedtitleheight/2}, + minipage boxed title=1.5cm, + boxed title style={% + colback=white, + size=fbox, + boxrule=1pt, + boxsep=2pt, + underlay={% + \coordinate (dotA) at ($(interior.west) + (-0.5pt,0)$); + \coordinate (dotB) at ($(interior.east) + (0.5pt,0)$); + \begin{scope} + \clip (interior.north west) rectangle ([xshift=3ex]interior.east); + \filldraw [white, blur shadow={shadow opacity=60, shadow yshift=-.75ex}, rounded corners=2pt] (interior.north west) rectangle (interior.south east); + \end{scope} + \begin{scope}[gray!80!black] + \fill (dotA) circle (2pt); + \fill (dotB) circle (2pt); + \end{scope} + }, + }, + #1, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% SELF MADE COMMANDS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\newcommand{\thm}[2]{\begin{Theorem}{#1}{}#2\end{Theorem}} +\newcommand{\cor}[2]{\begin{Corollary}{#1}{}#2\end{Corollary}} +\newcommand{\rvw}[2]{\begin{Review}{#1}{}#2\end{Review}} +\newcommand{\mthd}[2]{\begin{Method}{#1}{}#2\end{Method}} +\newcommand{\clm}[3]{\begin{claim}{#1}{#2}#3\end{claim}} +\newcommand{\wc}[2]{\begin{wconc}{#1}{}\setlength{\parindent}{1cm}#2\end{wconc}} +\newcommand{\thmcon}[1]{\begin{Theoremcon}{#1}\end{Theoremcon}} +\newcommand{\ex}[2]{\begin{Example}{#1}{}#2\end{Example}} +\newcommand{\dfn}[2]{\begin{Definition}[colbacktitle=red!75!black]{#1}{}#2\end{Definition}} +\newcommand{\dfnc}[2]{\begin{definition}[colbacktitle=red!75!black]{#1}{}#2\end{definition}} +\newcommand{\qs}[2]{\begin{question}{#1}{}#2\end{question}} +\newcommand{\pf}[2]{\begin{myproof}[#1]#2\end{myproof}} +\newcommand{\nt}[1]{\begin{note}#1\end{note}} + +\newcommand*\circled[1]{\tikz[baseline=(char.base)]{ + \node[shape=circle,draw,inner sep=1pt] (char) {#1};}} +\newcommand\getcurrentref[1]{% + \ifnumequal{\value{#1}}{0} + {??} + {\the\value{#1}}% +} +\newcommand{\getCurrentSectionNumber}{\getcurrentref{section}} +\newenvironment{myproof}[1][\proofname]{% + \proof[\bfseries #1: ]% +}{\endproof} + +\newcommand{\mclm}[2]{\begin{myclaim}[#1]#2\end{myclaim}} +\newenvironment{myclaim}[1][\claimname]{\proof[\bfseries #1: ]}{} + +\newcounter{mylabelcounter} + +\makeatletter +\newcommand{\setword}[2]{% + \phantomsection + #1\def\@currentlabel{\unexpanded{#1}}\label{#2}% +} +\makeatother + + + + +\tikzset{ + symbol/.style={ + draw=none, + every to/.append style={ + edge node={node [sloped, allow upside down, auto=false]{$#1$}}} + } +} + + +% deliminators +\DeclarePairedDelimiter{\abs}{\lvert}{\rvert} +\DeclarePairedDelimiter{\norm}{\lVert}{\rVert} + +\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil} +\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor} +\DeclarePairedDelimiter{\round}{\lfloor}{\rceil} + +\newsavebox\diffdbox +\newcommand{\slantedromand}{{\mathpalette\makesl{d}}} +\newcommand{\makesl}[2]{% +\begingroup +\sbox{\diffdbox}{$\mathsurround=0pt#1\mathrm{#2}$}% +\pdfsave +\pdfsetmatrix{1 0 0.2 1}% +\rlap{\usebox{\diffdbox}}% +\pdfrestore +\hskip\wd\diffdbox +\endgroup +} +\newcommand{\dd}[1][]{\ensuremath{\mathop{}\!\ifstrempty{#1}{% +\slantedromand\@ifnextchar^{\hspace{0.2ex}}{\hspace{0.1ex}}}% +{\slantedromand\hspace{0.2ex}^{#1}}}} +\ProvideDocumentCommand\dv{o m g}{% + \ensuremath{% + \IfValueTF{#3}{% + \IfNoValueTF{#1}{% + \frac{\dd #2}{\dd #3}% + }{% + \frac{\dd^{#1} #2}{\dd #3^{#1}}% + }% + }{% + \IfNoValueTF{#1}{% + \frac{\dd}{\dd #2}% + }{% + \frac{\dd^{#1}}{\dd #2^{#1}}% + }% + }% + }% +} +\providecommand*{\pdv}[3][]{\frac{\partial^{#1}#2}{\partial#3^{#1}}} +% - others +\DeclareMathOperator{\Lap}{\mathcal{L}} +\DeclareMathOperator{\Var}{Var} % varience +\DeclareMathOperator{\Cov}{Cov} % covarience +\DeclareMathOperator{\E}{E} % expected + +% Since the amsthm package isn't loaded + +% I prefer the slanted \leq +\let\oldleq\leq % save them in case they're every wanted +\let\oldgeq\geq +\renewcommand{\leq}{\leqslant} +\renewcommand{\geq}{\geqslant} + +% % redefine matrix env to allow for alignment, use r as default +% \renewcommand*\env@matrix[1][r]{\hskip -\arraycolsep +% \let\@ifnextchar\new@ifnextchar +% \array{*\c@MaxMatrixCols #1}} + + +%\usepackage{framed} +%\usepackage{titletoc} +%\usepackage{etoolbox} +%\usepackage{lmodern} + + +%\patchcmd{\tableofcontents}{\contentsname}{\sffamily\contentsname}{}{} + +%\renewenvironment{leftbar} +%{\def\FrameCommand{\hspace{6em}% +% {\color{myyellow}\vrule width 2pt depth 6pt}\hspace{1em}}% +% \MakeFramed{\parshape 1 0cm \dimexpr\textwidth-6em\relax\FrameRestore}\vskip2pt% +%} +%{\endMakeFramed} + +%\titlecontents{chapter} +%[0em]{\vspace*{2\baselineskip}} +%{\parbox{4.5em}{% +% \hfill\Huge\sffamily\bfseries\color{myred}\thecontentspage}% +% \vspace*{-2.3\baselineskip}\leftbar\textsc{\small\chaptername~\thecontentslabel}\\\sffamily} +%{}{\endleftbar} +%\titlecontents{section} +%[8.4em] +%{\sffamily\contentslabel{3em}}{}{} +%{\hspace{0.5em}\nobreak\itshape\color{myred}\contentspage} +%\titlecontents{subsection} +%[8.4em] +%{\sffamily\contentslabel{3em}}{}{} +%{\hspace{0.5em}\nobreak\itshape\color{myred}\contentspage} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% TABLE OF CONTENTS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\usepackage{tikz} +\definecolor{doc}{RGB}{0,60,110} +\usepackage{titletoc} +\contentsmargin{0cm} +\titlecontents{chapter}[3.7pc] +{\addvspace{30pt}% + \begin{tikzpicture}[remember picture, overlay]% + \draw[fill=doc!60,draw=doc!60] (-7,-.1) rectangle (-0.9,.5);% + \pgftext[left,x=-3.5cm,y=0.2cm]{\color{white}\Large\sc\bfseries Chapter\ \thecontentslabel};% + \end{tikzpicture}\color{doc!60}\large\sc\bfseries}% +{} +{} +{\;\titlerule\;\large\sc\bfseries Page \thecontentspage + \begin{tikzpicture}[remember picture, overlay] + \draw[fill=doc!60,draw=doc!60] (2pt,0) rectangle (4,0.1pt); + \end{tikzpicture}}% +\titlecontents{section}[3.7pc] +{\addvspace{2pt}} +{\contentslabel[\thecontentslabel]{2pc}} +{} +{\hfill\small \thecontentspage} +[] +\titlecontents*{subsection}[3.7pc] +{\addvspace{-1pt}\small} +{} +{} +{\ --- \small\thecontentspage} +[ \textbullet\ ][] + +\makeatletter +\renewcommand{\tableofcontents}{% + \chapter*{% + \vspace*{-20\p@}% + \begin{tikzpicture}[remember picture, overlay]% + \pgftext[right,x=15cm,y=0.2cm]{\color{doc!60}\Huge\sc\bfseries \contentsname};% + \draw[fill=doc!60,draw=doc!60] (13,-.75) rectangle (20,1);% + \clip (13,-.75) rectangle (20,1); + \pgftext[right,x=15cm,y=0.2cm]{\color{white}\Huge\sc\bfseries \contentsname};% + \end{tikzpicture}}% + \@starttoc{toc}} +\makeatother + diff --git a/6th-Semester-Spring-2024/TentativeSchedule.png 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