Start TP2

theorie-signal/exercices/tp2/Makefile

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+timestamp=$(shell date +%Y-%m-%d_%H:%M)
+
+all: tp2
+
+tp1: tp2.tex
+	@latexmk -pdf tp1.tex
+	@if ! cmp --silent build/tp2.pdf tp2_*.pdf; then \
+		touch tp2_tmp.pdf; \
+		rm tp2*.pdf; \
+		cp build/tp2.pdf tp2_${timestamp}.pdf; \
+		echo "Updated"; \
+	fi
+
+clean:
+	@rm -rf build 2>/dev/null

theorie-signal/exercices/tp2/code/x1.m

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+% x1
+
+fe = 10000;
+f1 = 100;
+
+Tps = [0 : 1/fe : 1 - 1/fe];
+x1 = sin(2*pi*f1*Tps);
+
+figure
+plot(Tps,x1);
+xlabel = "t";
+ylabel = "x1(t)";
+Title = "x1";
+
+Frq = [0 : fe/length(x1) : fe - fe/length(x1)];
+X1 = fft(x1);
+
+figure
+plot(Frq,abs(X1));
+xlabel = "f";
+ylabel = "Sx1(f)";
+Title = "Spectre de x1";

theorie-signal/exercices/tp2/code/x2.m

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+% x2
+
+fe = 10000;
+f1 = 100;
+f2 = 300;
+
+Tps = [0 : 1/fe : 1 - 1/fe];
+x2 = sin(2*pi*f1*Tps) + sin(2*pi*f2*Tps);
+
+figure
+plot(Tps,x2);
+xlabel = "t";
+ylabel = "x2(t)";
+Title = "x2";
+
+Frq = [0 : fe/length(x2) : fe - fe/length(x2)];
+X2 = fft(x2);
+
+figure
+plot(Frq,abs(X2));
+xlabel = "f";
+ylabel = "Sx2(f)";
+Title = "Spectre de x2";

theorie-signal/exercices/tp2/style.sty

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+\ProvidesPackage{style}
+
+\usepackage[
+    %showframe,
+    a4paper,includeheadfoot,margin=2cm,top=1cm,bottom=1cm
+]{geometry}
+
+\setcounter{tocdepth}{2}
+
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{babel}
+
+\usepackage{datetime}
+
+\usepackage{color}
+
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\everymath{\displaystyle}
+\newcommand*\dif{\mathop{}\!\mathrm{d}}
+
+\usepackage{booktabs}
+\usepackage{tabularx}
+\newcolumntype{Y}{>{\centering\arraybackslash}X}
+\usepackage{multicol}
+\usepackage{multirow}
+\usepackage{makecell}
+\usepackage{parskip}
+\usepackage{microtype}
+
+\usepackage{listingsutf8}
+\lstset{%
+    inputencoding=utf8/latin1,
+    basicstyle=\small\ttfamily,
+    columns=flexible,
+    breaklines=true,
+    extendedchars=true,
+    literate=
+    {á}{{\'a}}1 {é}{{\'e}}1 {í}{{\'\i}}1 {ó}{{\'o}}1 {ú}{{\'u}}1
+    {Á}{{\'A}}1 {É}{{\'E}}1 {Í}{{\'I}}1 {Ó}{{\'O}}1 {Ú}{{\'U}}1
+    {à}{{\`a}}1 {è}{{\`e}}1 {ì}{{\`\i}}1 {ò}{{\`o}}1 {ù}{{\`u}}1
+    {À}{{\`A}}1 {È}{{\`E}}1 {Ì}{{\`I}}1 {Ò}{{\`O}}1 {Ù}{{\`U}}1
+    {ä}{{\"a}}1 {ë}{{\"e}}1 {ï}{{\"\i}}1 {ö}{{\"o}}1 {ü}{{\"u}}1
+    {Ä}{{\"A}}1 {Ë}{{\"E}}1 {Ï}{{\"I}}1 {Ö}{{\"O}}1 {Ü}{{\"U}}1
+    {â}{{\^a}}1 {ê}{{\^e}}1 {î}{{\^\i}}1 {ô}{{\^o}}1 {û}{{\^u}}1
+    {Â}{{\^A}}1 {Ê}{{\^E}}1 {Î}{{\^I}}1 {Ô}{{\^O}}1 {Û}{{\^U}}1
+    {Ã}{{\~A}}1 {ã}{{\~a}}1 {Õ}{{\~O}}1 {õ}{{\~o}}1 {œ}{{\oe}}1
+    {Œ}{{\OE}}1 {æ}{{\ae}}1 {Æ}{{\AE}}1 {ß}{{\ss}}1 {ű}{{\H{u}}}1
+    {Ű}{{\H{U}}}1 {ő}{{\H{o}}}1 {Ő}{{\H{O}}}1 {ç}{{\c c}}1
+    {Ç}{{\c C}}1 {ø}{{\o}}1 {å}{{\r a}}1 {Å}{{\r A}}1
+    {€}{{\euro}}1 {£}{{\pounds}}1 {«}{{\guillemotleft}}1
+    {»}{{\guillemotright}}1 {ñ}{{\~n}}1 {Ñ}{{\~N}}1 {¿}{{?`}}1
+}
+\let\oldlstinputlisting\lstinputlisting
+% make \lstinputlisting always have frame
+\renewcommand{\lstinputlisting}[2][]{\oldlstinputlisting[frame=single,#1]{#2}}
+
+\lstnewenvironment{console}[1][]{%
+    \lstset{%
+        inputencoding=utf8/latin1,
+        basicstyle=\small\ttfamily\color{white},
+        columns=flexible,
+        breaklines=true,
+        extendedchars=true,
+        literate=
+        {á}{{\'a}}1 {é}{{\'e}}1 {í}{{\'\i}}1 {ó}{{\'o}}1 {ú}{{\'u}}1
+        {Á}{{\'A}}1 {É}{{\'E}}1 {Í}{{\'I}}1 {Ó}{{\'O}}1 {Ú}{{\'U}}1
+        {à}{{\`a}}1 {è}{{\`e}}1 {ì}{{\`\i}}1 {ò}{{\`o}}1 {ù}{{\`u}}1
+        {À}{{\`A}}1 {È}{{\`E}}1 {Ì}{{\`I}}1 {Ò}{{\`O}}1 {Ù}{{\`U}}1
+        {ä}{{\"a}}1 {ë}{{\"e}}1 {ï}{{\"\i}}1 {ö}{{\"o}}1 {ü}{{\"u}}1
+        {Ä}{{\"A}}1 {Ë}{{\"E}}1 {Ï}{{\"I}}1 {Ö}{{\"O}}1 {Ü}{{\"U}}1
+        {â}{{\^a}}1 {ê}{{\^e}}1 {î}{{\^\i}}1 {ô}{{\^o}}1 {û}{{\^u}}1
+        {Â}{{\^A}}1 {Ê}{{\^E}}1 {Î}{{\^I}}1 {Ô}{{\^O}}1 {Û}{{\^U}}1
+        {Ã}{{\~A}}1 {ã}{{\~a}}1 {Õ}{{\~O}}1 {õ}{{\~o}}1 {œ}{{\oe}}1
+        {Œ}{{\OE}}1 {æ}{{\ae}}1 {Æ}{{\AE}}1 {ß}{{\ss}}1 {ű}{{\H{u}}}1
+        {Ű}{{\H{U}}}1 {ő}{{\H{o}}}1 {Ő}{{\H{O}}}1 {ç}{{\c c}}1
+        {Ç}{{\c C}}1 {ø}{{\o}}1 {å}{{\r a}}1 {Å}{{\r A}}1
+        {€}{{\euro}}1 {£}{{\pounds}}1 {«}{{\guillemotleft}}1
+        {»}{{\guillemotright}}1 {ñ}{{\~n}}1 {Ñ}{{\~N}}1 {¿}{{?`}}1,
+        backgroundcolor=\color{black}, #1
+    }%
+}{}
+
+\usepackage{graphicx}
+
+\usepackage[hyphens]{url}
+\usepackage[colorlinks,hidelinks]{hyperref}
+
+\usepackage{letltxmacro}
+\LetLtxMacro{\normalparagraph}{\paragraph}
+\renewcommand{\paragraph}[1]{\normalparagraph{#1}\mbox{}}
+
+\sloppy

theorie-signal/exercices/tp2/tp2.tex

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+\documentclass[a4paper,french,12pt]{article}
+
+\title{
+Théorie du signal --- TP2
+\\ \large Décomposition en Série de Fourier
+}
+\author{Adam BELGHITH et Tunui FRANKEN}
+\date{Dernière compilation~: \today{} à \currenttime}
+
+\usepackage{style}
+\usepackage{enumitem}
+\usepackage{xfrac}
+\usepackage{tikz}
+\usepackage{float}
+
+\begin{document}
+
+\maketitle
+
+\section{Spectre d'un signal échantillonné}
+
+    Les figures obtenues confirment bien la théorie~: le spectre possède deux raies, celle de droite correspondant au symmétrique (négatif) de la raie de gauche, décalée d'une fréquence d'échantillonnage.
+    Nous avons donc deux raies~: $f_1$ et $f_e - f_1$.
+
+    \begin{figure}[H]
+        \includegraphics[width=\linewidth]{./img/x1_temporel.png}
+        \caption{$x_1(t) = \sin(2\pi f_1 t)$; $f_1 = 100Hz$}
+    \end{figure}
+    \begin{figure}[H]
+        \includegraphics[width=\linewidth]{./img/x2_temporel.png}
+        \caption{$x_2(t) = \sin(2\pi f_1 t) + \sin(2\pi f_2 t)$; $f_1 = 100Hz$; $f_2 = 300Hz$}
+    \end{figure}
+    \begin{figure}[H]
+        \includegraphics[width=\linewidth]{./img/x3_temporel.png}
+        \caption{$x_3(t) = \sin(2\pi f_1 t) + \sin(2\pi f_2 t)$; $f_1 = 2000Hz$; $f_2 = 7000Hz$}
+    \end{figure}
+
+\end{document}