\documentclass{report} \input{preamble} \input{macros} \input{letterfonts} \title{\Huge{Electrical Communication Systems}} \author{\huge{Aidan Sharpe}} \date{} \begin{document} \maketitle \newpage% or \cleardoublepage % \pdfbookmark[]{}{<dest>} \pdfbookmark[section]{\contentsname}{toc} \tableofcontents \pagebreak \chapter{} $$\boxed{\text{Source}} \to \boxed{\text{Transmitter}} \to \boxed{\text{Channel}} \to \boxed{\text{Receiver}} \to \boxed{\text{Sink}}$$ \section{The Fundamental Transmission Limit} \thm{Shannon's Theorem} { The theoretical limit for error-free transmission in a communications system in the presence of noise (the channel capacity) is a function of the channel bandwidth $B$ and the signal to noise power ration $S/N$. \begin{equation} C = B \log_2(1 + S/N) \end{equation} } \ex{Shannon's Theorem} { Given a 1[W] signal perturbed by 1[mW] of noise, the SNR is 1000. In dB, the SNR is \begin{equation} \text{dB} = 10 \log_{10}(\text{SNR}). \end{equation} In this case, the SNR is 30[dB]. } \end{document}