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3_comm.tex
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\documentclass[aspectratio=169]{beamer}
\usepackage{../styles/com303}
%\setbeameroption{show only notes}\def\logoEPFL{}
\setbeameroption{show notes}
\begin{document}
\intertitle{digital vs analog communications}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Data transmission and noise amplification
\def\tempFun{x 31 div 180 mul dup 1.1 mul cos 1 add 2 div exch 4 mul sin 0.1 mul add 10 mul x 20 div add 1.4 div 5 sub }
\def\atten{10 div }
\def\noise{rand 2147483647 div 0.5 sub 0.2 mul add }
\def\ampli{10 mul }
\begin{frame} \frametitle{Data transmission}
\begin{center}
\begin{figure}
\begin{dspBlocks}{2}{0}
TX~~ & \BDfilter{channel} & ~~RX
\ncline{->}{1,1}{1,2}\ncline{->}{1,2}{1,3}
\end{dspBlocks}
\end{figure}
\end{center}
\end{frame}
\begin{frame} \frametitle{What happens to analog signals}
\begin{center}
\begin{figure}
\begin{dspBlocks}{2}{1}
$x(t)$~~ & & \BDadd & ~~$\hat{x}(t)$ \\
& & \raisebox{-1.2em}{$\sigma(t)$}
\ncline{->}{1,1}{1,3}\taput{$1/G$}
\ncline{->}{1,3}{1,4}
\ncline{->}{2,3}{1,3}
\end{dspBlocks}
\end{figure}
\vspace{3em}
$\hat{x}(t) = x(t)/G + \sigma(t)$
\end{center}
\end{frame}
\begin{frame} \frametitle{What happens to analog signals}
\begin{center}
\begin{figure}
\begin{dspPlot}[yticks=5,xticks=none,sidegap=0]{0,100}{-7,7}
\moocStyle
\only<1>{\dspFunc{\tempFun}}
\only<2>{\dspFunc{\tempFun \atten}}
\only<3>{\dspFunc{\tempFun \atten \noise}}
\end{dspPlot}
\end{figure}
\only<1>{$x(t)$}
\only<2>{$x(t)/G$}
\only<3>{$x(t)/G + \sigma(t)$}
\end{center}
\end{frame}
\begin{frame} \frametitle{We can amplify to compensate attenuation}
\begin{center}
\begin{figure}
\begin{dspBlocks}{2}{1}
$x(t)$~~ & & \BDadd & ~~$\hat{x}_1(t)$ \\
& & \raisebox{-1.2em}{$\sigma(t)$}
\ncline{->}{1,1}{1,3}\taput{$1/G$}
\ncline{->}{1,3}{1,4}\taput{{\color{red}$G$}}
\ncline{->}{2,3}{1,3}
\end{dspBlocks}
\end{figure}
\vspace{3em}
but: $\hat{x}_1(t) = x(t) + {\color{red}G}\sigma(t)$
\end{center}
\end{frame}
\begin{frame} \frametitle{Transmission of analog signals}
\begin{center}
\begin{figure}
\begin{dspPlot}[yticks=5,xticks=none,sidegap=0]{0,100}{-7,7}
\moocStyle
\only<1>{\dspFunc{\tempFun \atten \noise}}
\only<2>{\dspFunc{\tempFun \atten \noise \ampli}}
\end{dspPlot}
\end{figure}
\only<1>{$x(t)/G + \sigma(t)$}
\only<2>{$\hat{x}_1(t) = G[x(t)/G + \sigma(t)] = x(t) + G\sigma(t)$}
\end{center}
\end{frame}
%% Atlantic cables
\begin{frame}[plain]
\begin{columns}[c]
\begin{column}{\paperwidth}
\includegraphics[width=\paperwidth,height=\paperheight]{Atlantic_cable_Map.eps}
\par
\end{column}
\end{columns}
\end{frame}
%% Agamemnon
\begin{frame}[plain]
\begin{columns}[c]
\begin{column}{\paperwidth}
\includegraphics[width=\paperwidth,height=\paperheight]{agam.ps}
\par
\end{column}
\end{columns}
\end{frame}
\begin{frame} \frametitle{Transmitting a signal overseas}
\begin{center}
For a long, long channel we need repeaters
\vspace{1em}
\begin{figure}
\def\ns{\raisebox{-1.2em}{$\sigma(t)$}}
\begin{dspBlocks}{1}{0.5}
% 1 2 3 4 5 6 7 8 \
$x(t)$~~ & \BDadd & ~$\hat{x}_1(t)$~ & \BDadd & ~$\ldots$~ & \BDadd & ~~$\hat{x}_N(t)$ \\
& \ns & & \ns & & \ns
\BDConnH{1}{1}{2}{$1/G$}
\BDConnH{1}{2}{3}{$G$}
\BDConnH{1}{3}{4}{$1/G$}
\BDConnH{1}{4}{5}{$G$}
\BDConnH{1}{5}{6}{$1/G$}
\BDConnH{1}{6}{7}{$G$}
\BDConnV{2}{2}{1}{}
\BDConnV{2}{4}{1}{}
\BDConnV{2}{6}{1}{}
\end{dspBlocks}
\end{figure}
\vspace{3em}
$\hat{x}_N(t) = x(t) + NG\sigma(t)$
\end{center}
\end{frame}
%%Here a slide about long distance communication and repeaters
%\begin{frame}
% \frametitle{Long distance communication}
% \begin{itemize}
% \item Transoceanic cable:
% \begin{itemize}
% \item Cable too long for single transmission
% \item Necessary to have repeaters
% \end{itemize}
% \pause
% \item Block diagram
% \begin{itemize}
% \item Single line with loss of $\alpha$ and noise $\sigma^2$
% \item $N$ pieces with loss of $\alpha/N$ and noise $\sigma^2/N$ (?)
% \item Amplifiers at relays
% \end{itemize}
% \end{itemize}
%\end{frame}
%% Noise amplification
\begin{frame} \frametitle{Transmission of analog signals}
\begin{center}
\begin{figure}
\begin{dspPlot}[yticks=5,xticks=none,sidegap=0]{0,100}{-7,7}
\moocStyle
\only<1>{\dspFunc{\tempFun}}
\only<2>{\dspFunc{\tempFun \atten \noise}}
\only<3>{\dspFunc{\tempFun \atten \noise \ampli}}
\only<4>{\dspFunc{\tempFun \atten \noise \ampli \atten \noise}}
\only<5>{\dspFunc{\tempFun \atten \noise \ampli \atten \noise \ampli}}
\only<6>{\dspFunc{\tempFun \atten \noise \ampli \atten \noise \ampli \atten \noise \ampli \atten \noise \ampli \atten \noise \ampli \atten \noise \ampli}}
\end{dspPlot}
\end{figure}
\only<1>{$x(t)$}
\only<2>{$x(t)/G + \sigma(t)$}
\only<3>{$\hat{x}_1(t) = G[x(t)/G + \sigma(t)] = x(t) + G\sigma(t)$}
\only<4>{$\hat{x}_1(t)/G + \sigma(t)$}
\only<5>{$\hat{x}_2(t) = G[\hat{x}_1(t)/G + \sigma(t)] = x(t) + 2G\sigma(t)$}
\only<6>{$\hat{x}_N(t) = x(t) + NG\sigma(t)$}
\end{center}
\end{frame}
\begin{frame} \frametitle{In digital signals we can threshold}
\begin{center}
\begin{figure}
\begin{dspBlocks}{2}{1}
$x(t)$~~ & & \BDadd & \BDfilter{$|\cdot|$} & ~~$\hat{x}_1(t)$ \\
& & \raisebox{-1.2em}{$\sigma(t)$}
\ncline{->}{1,1}{1,3}\taput{$1/G$}
\ncline{->}{1,3}{1,4}\taput{$G$}
\ncline{->}{1,4}{1,5}
\ncline{->}{2,3}{1,3}
\end{dspBlocks}
\end{figure}
\vspace{3em}
$\hat{x}_1(t) = \mbox{sgn}[x(t) + G\sigma(t)]$
\end{center}
\end{frame}
%% Rectification
\def\binFun{x 23 div cvi 2 mod -2 mul 1 add 5 mul }
\begin{frame} \frametitle{Transmission of quantized signals}
\begin{center}
\begin{figure}
\begin{dspPlot}[yticks=5,xticks=none,sidegap=0]{0,99}{-7,7}
\moocStyle
\only<1>{\dspFunc{\binFun}}
\only<2>{\dspFunc{\binFun \atten \noise}}
\only<3>{\dspFunc{\binFun \atten \noise \ampli}}
\only<4>{\dspFunc{\binFun}}
\end{dspPlot}
\end{figure}
\only<1>{$x(t)$}
\only<2>{$x(t)/G + \sigma(t)$}
\only<3>{$G[x(t)/G + \sigma(t)] = x(t) + G\sigma(t)$}
\only<4>{$\hat{x}_1(t) = 5\,\mbox{sgn}[x(t) + G\sigma(t)]$}
\end{center}
\end{frame}
\begin{frame} \frametitle{Digital data throughputs}
\begin{itemize}
\item Transatlantic cable:
\begin{itemize}
\item 1866: 8 words per minute ($\approx$5 bps)
\item 1956: AT\&T, coax, 48 voice channels ($\approx$3Mbps)
\item 2005: Alcatel Tera10, fiber, 8.4 Tbps ($8.4\times 10^{12}$ bps)
\item 2012: fiber, 60 Tbps
\end{itemize}
\pause
\item Voiceband modems
\begin{itemize}
\item 1950s: Bell 202, 1200 bps
\item 1990s: V90, 56Kbps
\item 2008: ADSL2+, 24Mbps
\end{itemize}
\end{itemize}
\end{frame}
\cueCard{let's try this in Python...}
\end{document}

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