\documentclass{report}

\input{preamble}
\input{macros}
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\title{\Huge{Electrical Communication Systems}}
\author{\huge{Aidan Sharpe}}
\date{}

\begin{document}

\maketitle
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\tableofcontents
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\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}
