diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.aux b/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.aux index 3669b4c..9ac9bb1 100644 --- a/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.aux +++ b/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.aux @@ -7,7 +7,8 @@ \providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}} \newlabel{fig:N_point_DFT}{{1}{1}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}The Z-Transform}{1}{}\protected@file@percent } -\newlabel{fig:9_point_DFT}{{\caption@xref {fig:9_point_DFT}{ on input line 62}}{2}} +\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces The 9-point DFT of $x[n]$, where $N=8$\relax }}{2}{}\protected@file@percent } +\newlabel{fig:9_point_DFT}{{2}{2}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3}The Inverse Z-Transform}{2}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {2}Conclusions}{2}{}\protected@file@percent } -\gdef \@abspage@last{3} +\@writefile{toc}{\contentsline {section}{\numberline {2}Conclusions}{3}{}\protected@file@percent } +\gdef \@abspage@last{4} diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.fdb_latexmk b/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.fdb_latexmk index 0c6933c..c6a49f9 100644 --- a/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.fdb_latexmk +++ b/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.fdb_latexmk @@ -1,5 +1,5 @@ # Fdb version 4 -["pdflatex"] 1713397604.9034 "lab-4.tex" "lab-4.pdf" "lab-4" 1713397605.40716 0 +["pdflatex"] 1713402655.49744 "lab-4.tex" "lab-4.pdf" "lab-4" 1713402656.21445 0 "/usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1246382020 1004 54797486969f23fa377b128694d548df "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm" 1246382020 988 bdf658c3bfc2d96d3c8b02cfc1c94c20 "" @@ -9,7 +9,6 @@ "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm" 1246382020 908 2921f8a10601f252058503cc6570e581 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm5.tfm" 1246382020 940 75ac932a52f80982a9f8ea75d03a34cf "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm" 1246382020 940 228d6584342e91276bf566bcf9716b83 "" - "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmbx10.tfm" 1136768653 1328 c834bbb027764024c09d3d2bf908b5f0 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm" 1136768653 1324 c910af8c371558dc20f2d7822f66fe64 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmex10.tfm" 1136768653 992 662f679a0b3d2d53c1b94050fdaa3f50 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmmi12.tfm" 1136768653 1524 4414a8315f39513458b80dfc63bff03a "" @@ -22,7 +21,7 @@ "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmsy10.tfm" 1136768653 1124 6c73e740cf17375f03eec0ee63599741 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmsy6.tfm" 1136768653 1116 933a60c408fc0a863a92debe84b2d294 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmsy8.tfm" 1136768653 1120 8b7d695260f3cff42e636090a8002094 "" - "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb" 1248133631 34811 78b52f49e893bcba91bd7581cdc144c0 "" + "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmtt10.tfm" 1136768653 768 1321e9409b4137d6fb428ac9dc956269 "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb" 1248133631 32080 340ef9bf63678554ee606688e7b5339d "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb" 1248133631 30251 6afa5cb1d0204815a708a080681d4674 "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb" 1248133631 36299 5f9df58c2139e7edcf37c8fca4bd384d "" @@ -31,10 +30,12 @@ "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb" 1248133631 35752 024fb6c41858982481f6968b5fc26508 "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb" 1248133631 32722 d7379af29a190c3f453aba36302ff5a9 "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb" 1248133631 32362 179c33bbf43f19adbb3825bb4e36e57a "" + "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr5.pfb" 1248133631 31809 8670ca339bf94e56da1fc21c80635e2a "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb" 1248133631 32762 224316ccc9ad3ca0423a14971cfa7fc1 "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb" 1248133631 32569 5e5ddc8df908dea60932f3c484a54c0d "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb" 1248133631 32716 08e384dc442464e7285e891af9f45947 "" - "/usr/share/texlive/texmf-dist/tex/context/base/mkii/supp-pdf.mkii" 1689984000 71627 94eb9990bed73c364d7f53f960cc8c5b "" + "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt10.pfb" 1248133631 31099 c85edf1dd5b9e826d67c9c7293b6786c "" + "/usr/share/texlive/texmf-dist/tex/context/base/mkii/supp-pdf.mkii" 1684972800 71627 94eb9990bed73c364d7f53f960cc8c5b "" "/usr/share/texlive/texmf-dist/tex/generic/iftex/iftex.sty" 1644112042 7237 bdd120a32c8fdb4b433cf9ca2e7cd98a "" "/usr/share/texlive/texmf-dist/tex/generic/iftex/ifvtex.sty" 1572645307 1057 525c2192b5febbd8c1f662c9468335bb "" "/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty" 1359763108 5949 3f3fd50a8cc94c3d4cbf4fc66cd3df1c "" @@ -45,11 +46,11 @@ "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty" 1654720880 88393 1adf6fa3f245270d06e3d4f8910f7fc5 "" "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty" 1654720880 4474 f04cd1cc7bd76eb033e6fb12eb6a0d77 "" "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty" 1654720880 2444 70065bddd85997dc1fd0bb7ae634e5fa "" - "/usr/share/texlive/texmf-dist/tex/latex/base/article.cls" 1689984000 20144 d5ecf0a5140c8d8d8b72cbe86e320eff "" - "/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo" 1689984000 8448 c33a4e1cb35cee9b33c2b21033b73e39 "" - "/usr/share/texlive/texmf-dist/tex/latex/caption/caption.sty" 1678653221 55778 14d5c99aa26410e440820bb9ea5b8b3a "" - "/usr/share/texlive/texmf-dist/tex/latex/caption/caption3.sty" 1678653221 71836 1a735454ad10692452eb2f2fc37f3865 "" - "/usr/share/texlive/texmf-dist/tex/latex/caption/subcaption.sty" 1678653221 12462 ecf33913ce1e8012075d24e1f47f0d9b "" + "/usr/share/texlive/texmf-dist/tex/latex/base/article.cls" 1684972800 20144 7555b7429d80bef287ebb82117811acc "" + "/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo" 1684972800 8448 e0391042ca0932ede1098ae14ada60ba "" + "/usr/share/texlive/texmf-dist/tex/latex/caption/caption.sty" 1647548653 54291 b8e5c600d4aa37b48a740dd2a6c26163 "" + "/usr/share/texlive/texmf-dist/tex/latex/caption/caption3.sty" 1647548653 71241 d2cd3a1c5acef9cb31f945b93c0bb6e3 "" + "/usr/share/texlive/texmf-dist/tex/latex/caption/subcaption.sty" 1645391520 11546 6c5257d230d8c5626812b45bc2f31212 "" "/usr/share/texlive/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty" 1579991033 13886 d1306dcf79a944f6988e688c1785f9ce "" "/usr/share/texlive/texmf-dist/tex/latex/float/float.sty" 1137110151 6749 16d2656a1984957e674b149555f1ea1d "" "/usr/share/texlive/texmf-dist/tex/latex/geometry/geometry.sty" 1578002852 41601 9cf6c5257b1bc7af01a58859749dd37a "" @@ -59,18 +60,18 @@ "/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty" 1654720880 8010 a8d949cbdbc5c983593827c9eec252e1 "" "/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty" 1654720880 2671 7e67d78d9b88c845599a85b2d41f2e39 "" "/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty" 1654720880 4023 293ea1c16429fc0c4cf605f4da1791a9 "" - 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file:line:error style messages enabled. %&-line parsing enabled. **lab-4.tex (./lab-4.tex -LaTeX2e <2022-11-01> patch level 1 -L3 programming layer <2023-02-22> (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls -Document Class: article 2022/07/02 v1.4n Standard LaTeX document class +LaTeX2e <2022-06-01> patch level 5 +L3 programming layer <2022-12-17> +(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls +Document Class: article 2021/10/04 v1.4n Standard LaTeX document class (/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo -File: size10.clo 2022/07/02 v1.4n Standard LaTeX file (size option) +File: size10.clo 2021/10/04 v1.4n Standard LaTeX file (size option) ) \c@part=\count185 \c@section=\count186 @@ -19,24 +19,28 @@ File: size10.clo 2022/07/02 v1.4n Standard LaTeX file (size option) \c@subparagraph=\count190 \c@figure=\count191 \c@table=\count192 -\abovecaptionskip=\skip48 -\belowcaptionskip=\skip49 +\abovecaptionskip=\skip47 +\belowcaptionskip=\skip48 \bibindent=\dimen140 -) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty +) +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty Package: amsmath 2022/04/08 v2.17n AMS math features -\@mathmargin=\skip50 +\@mathmargin=\skip49 For additional information on amsmath, use the `?' option. 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Use iftex instead. - (/usr/share/texlive/texmf-dist/tex/generic/iftex/iftex.sty + +(/usr/share/texlive/texmf-dist/tex/generic/iftex/iftex.sty Package: iftex 2022/02/03 v1.0f TeX engine tests )) \Gm@cnth=\count284 @@ -182,11 +201,13 @@ Package: iftex 2022/02/03 v1.0f TeX engine tests \Gm@layouthoffset=\dimen170 \Gm@layoutvoffset=\dimen171 \Gm@dimlist=\toks25 -) (/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def -File: l3backend-pdftex.def 2023-01-16 L3 backend support: PDF output (pdfTeX) +) +(/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def +File: l3backend-pdftex.def 2022-10-26 L3 backend support: PDF output (pdfTeX) \l__color_backend_stack_int=\count287 \l__pdf_internal_box=\box57 -) (./lab-4.aux) +) +(./lab-4.aux) \openout1 = `lab-4.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 19. @@ -203,7 +224,8 @@ LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 19. LaTeX Font Info: ... okay on input line 19. 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LaTeX Font Info: ... okay on input line 19. - (/usr/share/texlive/texmf-dist/tex/context/base/mkii/supp-pdf.mkii + +(/usr/share/texlive/texmf-dist/tex/context/base/mkii/supp-pdf.mkii [Loading MPS to PDF converter (version 2006.09.02).] \scratchcounter=\count288 \scratchdimen=\dimen172 @@ -218,9 +240,12 @@ LaTeX Font Info: ... okay on input line 19. \everyMPtoPDFconversion=\toks27 ) (/usr/share/texlive/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty Package: epstopdf-base 2020-01-24 v2.11 Base part for package epstopdf -Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 485. - (/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg -File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live +Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 4 +85. + +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg +File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv +e )) \c@lstlisting=\count294 Package caption Info: Begin \AtBeginDocument code. @@ -262,11 +287,14 @@ Package caption Info: End \AtBeginDocument code. * (1in=72.27pt=25.4mm, 1cm=28.453pt) LaTeX Font Info: Trying to load font information for U+msa on input line 21. + (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd File: umsa.fd 2013/01/14 v3.01 AMS symbols A ) LaTeX Font Info: Trying to load font information for U+msb on input line 21. - (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd + + +(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd File: umsb.fd 2013/01/14 v3.01 AMS symbols B ) [1 @@ -285,13 +313,6 @@ File: N8_point_DFT.png Graphic file (type png) Package pdftex.def Info: N8_point_DFT.png used on input line 54. (pdftex.def) Requested size: 234.8775pt x 176.15768pt. - -Package caption Warning: \label without proper reference on input line 62. -See the caption package documentation for explanation. - - -LaTeX Warning: Reference `fig:9_point_DFT' on page 1 undefined on input line 58. - File: Q9_point_DFT.png Graphic file (type png) @@ -300,24 +321,37 @@ Package pdftex.def Info: Q9_point_DFT.png used on input line 61. LaTeX Warning: `h' float specifier changed to `ht'. -[1 <./N8_point_dft.png>] [2 <./Q9_point_dft.png>] (./lab-4.aux) -LaTeX Warning: There were undefined references. +Underfull \hbox (badness 10000) in paragraph at lines 71--76 - ) + [] + +[1 <./N8_point_dft.png>] [2 <./Q9_point_dft.png>] [3] (./lab-4.aux) ) Here is how much of TeX's memory you used: - 5601 strings out of 476041 - 90928 string characters out of 5793174 - 1860388 words of memory out of 6000000 - 26020 multiletter control sequences out of 15000+600000 - 520150 words of font info for 63 fonts, out of 8000000 for 9000 + 5569 strings out of 476182 + 90423 string characters out of 5796582 + 1859793 words of memory out of 6000000 + 25843 multiletter control sequences out of 15000+600000 + 520010 words of font info for 63 fonts, out of 8000000 for 9000 1137 hyphenation exceptions out of 8191 - 57i,8n,63p,320b,347s stack positions out of 10000i,1000n,20000p,200000b,200000s - -Output written on lab-4.pdf (3 pages, 146760 bytes). + 55i,8n,63p,490b,340s stack positions out of 10000i,1000n,20000p,200000b,200000s + + +Output written on lab-4.pdf (4 pages, 162298 bytes). PDF statistics: - 79 PDF objects out of 1000 (max. 8388607) - 45 compressed objects within 1 object stream + 87 PDF objects out of 1000 (max. 8388607) + 50 compressed objects within 1 object stream 0 named destinations out of 1000 (max. 500000) 11 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.pdf b/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.pdf index df45693..acd6f06 100644 Binary files a/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.pdf and b/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.pdf differ diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.synctex.gz b/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.synctex.gz deleted file mode 100644 index f15d8ad..0000000 Binary files a/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.synctex.gz and /dev/null differ diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.tex b/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.tex index b43aaae..80d412a 100644 --- a/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.tex +++ b/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab-4.tex @@ -48,7 +48,7 @@ where $r$ is the common ratio between adjacent terms. For the $N$-point DFT of $ \end{cases}. \label{eqn:DFT_N_point} \end{equation} -The $N$-point DFT of $x[n]$, where $N=8$ is seen in figure \ref{fig:N_point_DFT}. It only has a non-zero value for $k={N\over2}=4$. This is the case for all even-number-point DFTs. Therefore only odd-number-point DFTs should be used. +The $N$-point DFT of $x[n]$, where $N=8$ is seen in figure \ref{fig:N_point_DFT}. It only has a non-zero value for $k={N\over2}=4$. This is the case for all even-number-point DFTs. Therefore, only odd-number-point DFTs should be used. \begin{figure}[h] \center \includegraphics[width=0.5\textwidth]{N8_point_DFT.png} @@ -57,21 +57,39 @@ The $N$-point DFT of $x[n]$, where $N=8$ is seen in figure \ref{fig:N_point_DFT} \end{figure} For example, the 9-point DFT of $x[n]$, where $N=8$ is seen in figure \ref{fig:9_point_DFT}. While equation \ref{eqn:DFT_N_point} cannot be used because there are a different number of samples for the DFT and the input signal, the overall DFT is more useful than the 8-point DFT. \begin{figure}[h] - \center + \center \includegraphics[width=0.5\textwidth]{Q9_point_DFT.png} + \caption{The 9-point DFT of $x[n]$, where $N=8$} \label{fig:9_point_DFT} \end{figure} - \subsection{The Z-Transform} Given a discrete signal, $x[n]$, its z-transform is given by \begin{equation} X(z) = \sum_n x[n] z^{-n} \end{equation} -where $z$ is a complex variable. +where $z$ is a complex variable. The Z-transform of any discrete signal is a continuous function. Therefore, any attempt to calculate the Z-transform with a digital computer requires sampling or symbolic math. Symbolic math is quite a powerful tool, and others have worked hard to implement the Z-transform as a symbolic function. In MATLAB, this function is \verb|ztrans|. +\\ +\\ +The Z-transform of the following signals can be found very quickly using this method: +$$x_1[n] = a^n u[n]$$ +$$x_2[n] = (n+1)a^n u[n]$$ +$$x_3[n] = a^n \cos(bn) u[n]$$ +$$\mathcal{Z}\{x_1[n]\} = -{z \over a - z}$$ +$$\mathcal{Z}\{x_2[n]\} = {az \over (a - z)^2} - {z \over a - 2}$$ +$$\mathcal{Z}\{x_3[n]\} = -{z(\cos(b) - z/a) \over a{z^2\over a^2} - {2z\cos(b) \over a} + 1}$$ \subsection{The Inverse Z-Transform} +Similarly, the inverse Z-transform also benefits from using a symbolic calculator. For example, the inverse Z-transform of the following can be found rapidly: +$$\mathcal{Z}\{x_4[n]\} = {z \over z + 0.5}$$ +$$\mathcal{Z}\{x_5[n]\} = {z^2 \over (z-0.8)^2}$$ +$$\mathcal{Z}\{x_6[n]\} = {z \over (z+0.3)(z+0.6)^2}$$ +$$x_4[n] = (-1/2)^n$$ +$$x_5[n] = 2(4/5)^n (n-1)(4/5)^n$$ +$$x_6[n] = {50n(-3/5)^n - 100(-3/5)^n + 100(-3/10)^n \over 9}$$ + \section{Conclusions} +Overall understanding tricks for calculating geometric sums is very helpful for calculating DFTs. It is also important to use odd-number-point DFTs only, as taking an even number of samples forces almost all values to go to zero. As for Z-transforms and inverse Z-transforms, knowing how to use symbolic computation makes finding them quite easy. Additionally, symbolic computation allows for the easy manipulation of how simplified or expanded the result is. \end{document} diff --git a/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab4_2.m b/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab4_2.m index 4b83ee2..d5ce4c3 100644 --- a/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab4_2.m +++ b/6th-Semester-Spring-2024/DSP/Labs/Lab-04/lab4_2.m @@ -1,9 +1,9 @@ syms n a b % Signals to take the z-transform of -f_a = a^n; -f_b = (n+1)*a^n*heaviside(n) -f_c = a^n*cos(b*n)*heaviside(n) +f_a = a^n +f_b = (n+1)*a^n +f_c = a^n*cos(b*n) % Take the z-transforms F_a = ztrans(f_a) diff --git a/6th-Semester-Spring-2024/SysCon/Final Project/Draft1.net b/6th-Semester-Spring-2024/SysCon/Final Project/Draft1.net deleted file mode 100644 index 56540b6..0000000 --- a/6th-Semester-Spring-2024/SysCon/Final Project/Draft1.net +++ /dev/null @@ -1,14 +0,0 @@ -* C:\users\sharpe\Documents\Rowan\Rowan-Classes\6th-Semester-Spring-2024\SysCon\Final Project\Draft1.asc -V1 N002 0 500 -R1 N004 0 1000 -L1 N003 N004 500µ -C1 N004 0 470µ -D1 0 N003 D -S1 N003 N002 N001 0 Switch1 -V2 N001 0 PULSE(0 5 0 0 0 2.4u 4u) -.model D D -.lib C:\users\sharpe\AppData\Local\LTspice\lib\cmp\standard.dio -.tran 1 -.model Switch1 SW(Ron=1 Roff=1Meg Vt=0.5 Vh=-0.4) -.backanno -.end