Homec4science
Diffusion epfl (master) Browse

R2653/teaching/MOOC/06 - 2016/lectures/02 basic/lecture_2.2a.tex
0117e6e16122master

Last Change
Raw File

lecture_2.2a.tex
View Options

\documentclass[aspectratio=169]{beamer}
\def\stylepath{../styles}
\usepackage{\stylepath/dspmooc}
\usepackage{hyperref}
\usepackage{verbatim}
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\lect{1}
\title[Lecture 2.2a:]{How your PC plays discrete-time sounds}
\date{}
\maketitle
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} \frametitle{The discrete-time sinusoid}
\begin{center}
$x[n] = \sin(\omega_0 n + \theta)$
\begin{dspPlot}[yticks=1,xticks=5]{-16, 16}{-1.2, 1.2}
\moocStyle
\dspSignal{x 3.14 mul 10 div RadtoDeg cos}
\end{dspPlot}
\end{center}
\end{frame}
\begin{frame} \frametitle{Digital vs physical frequency}
\begin{itemize}
\item Discrete time:
\begin{itemize}
\item $n$: no physical dimension (just a counter)
\item periodicity: how many samples before pattern repeats
\end{itemize}
\vspace{1em}
\pause
\item Physical world:
\begin{itemize}
\item periodicity: how many {\em seconds} before pattern repeats
\item frequency measured in Hz ($s^{-1})$
\end{itemize}
\end{itemize}
\end{frame}
\begin{frame} \frametitle{How your PC plays sounds}
\setbeamercovered{invisible}
\begin{center}
\begin{figure}
\begin{dspBlocks}{2}{1}
$x[n]~~$ & \BDfilter{sound card} & \raisebox{-1.2em}{\includegraphics[height=6em]{speaker.eps}} \\
\uncover<2>{ & [mnode=circle] {\color{red} $T_s$} & \hspace{-5cm} {\em system clock} \\
\ncline{->}{2,2}{1,2}}
\ncline{->}{1,1}{1,2}\ncline{->}{1,2}{1,3}
\end{dspBlocks}
\end{figure}
\end{center}
\end{frame}
\begin{frame} \frametitle{Digital vs physical frequency}
\begin{itemize}[<+->]
\item set $T_s$, time in seconds between samples
\item periodicity of $M$ samples $\longrightarrow$ periodicity of $MT_s$ seconds
\vspace{1em}
\item real world frequency:
\[
f = \frac{1}{MT_s} \mbox{Hz}
\]
\end{itemize}
\end{frame}
\begin{frame} \frametitle{Digital vs physical frequency}
\begin{itemize}
\item usually we choose $F_s$ the number of samples per seconds
\item $T_s = 1/F_s$
\end{itemize}
\vspace{2em}
\pause
\centering
E.g for a typical value $F_s = 48000$, $T_s \approx 20.8\mu s$. If $M=110$
\[
f \approx 440 \mbox{Hz}
\]
\end{frame}
\end{document}
c4science · Help