\documentclass[11pt,twoside,a4paper]{book}

\usepackage{amsfonts,amssymb,amsmath,atbegshi,bm,color,framed,lmodern,mathrsfs,microtype,pgfplots,subfigure,tikz,xspace}
\usepackage[amsmath,framed,thmmarks,hyperref]{ntheorem}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[frenchb]{babel}
\usepackage[hyperindex,colorlinks=true,citecolor=violet,linkcolor=bleufonce,frenchlinks=true]{hyperref}

\definecolor{violet}{rgb}{0.6,0.0,0.6}
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% TikZ and co
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\microtypecontext{kerning=french}

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\theoremindent0mm
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\setlength{\theorempostskipamount}{0mm}
\theoremstyle{break}

\newtheorem{definition}{Définition}%[section]
\theoremstyle{nonumberbreak}
\newtheorem{rema}{Remarque}
\newtheorem{remas}{Remarques}

\theoremstyle{break}
\newtheorem{thm}{Théorème}
\newtheorem{prop}{Proposition}

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\theorembodyfont{\normalfont}
\theoremsymbol{\ensuremath{\diamondsuit}}
\newtheorem{preuve}{Preuve}

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\theoremheaderfont{\sc}
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\theoremsymbol{}
\newframedtheorem{exemple}{Exemple}

\providecommand{\abs}[1]{\left\lvert#1\right\rvert}
\providecommand{\ud}{\mathrm{d}}
\providecommand{\norm}[1]{\lVert#1\rVert}
\providecommand{\esp}[1]{\mathrm{E}\!\left\{#1\right\}}
\providecommand{\sinc}{\,\mathrm{sinc}}
\providecommand{\sign}{\text{sign}}
\providecommand{\rect}{\mathrm{rect}}
\providecommand{\re}[1]{\mathrm{Re}\left\{#1\right\}}
\providecommand{\im}[1]{\mathrm{Im}\left\{#1\right\}}
\providecommand{\paireTF}{\stackrel{\mathcal{F}}{\longleftrightarrow}}
\providecommand{\Fo}[1]{\mathcal{F}\left\{#1\right\}}
\providecommand{\FoI}[1]{\mathcal{F}^{-1}\left\{#1\right\}}
\providecommand{\paireTL}{\stackrel{\mathcal{L}}{\longleftrightarrow}}
\providecommand{\La}[1]{\mathcal{L}\left\{#1\right\}}

\setcounter{secnumdepth}{3}
\renewcommand{\thesubsubsection}{(\alph{subsubsection})}

\setlength{\parindent}{0pt}
\setlength{\parskip}{6pt}

\title{Example}
\author{Version $\beta$}



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\begin{document}
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\maketitle

\tableofcontents

\chapter*{chapter name}\label{cha:chapter_name}

Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.

Bibliographie: \cite{Coulon-1984,Oppenheim-1983,Auger-1999,Jackson-1991,Schwartz-1966}.



\chapter{chapter name}\label{cha:chapter_name}

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\section{section name}\label{sec:section_name}

\subsection{subsection name}\label{sub:subsection_name}


\begin{definition}[Lorem]
	Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
\end{definition}



%
\begin{figure}
	\centering
	\subfigure[Signal déterministe.]{
	\begin{tikzpicture}[domain=-2.6:2.6]
		\draw[-stealth]	(-2.8,   0) -- (0, 0) node[below right] {$0$} -- (2.8, 0) node[right] {$t$};
		\draw[-stealth]	( 0,-1.5) -- (0, 1.5);
		\draw[very thick] plot[smooth,samples=100] function{sin(3*pi*x)/2+cos(pi*x)/2};
	\end{tikzpicture}
	\label{fig:deterministe}
	}%
	\subfigure[Signal aléatoire.]{
	\begin{tikzpicture}[domain=-2.6:2.6]
		\draw[-stealth]	(-2.8,   0) -- (0, 0) node[below left] {$0$} -- (2.8, 0) node[right] {$t$};
		\draw[-stealth]	( 0,-1.5) -- (0, 1.5);
		\draw[very thick] plot[smooth,samples=100] function{2*(rand(0)-0.5)};
	\end{tikzpicture}
	\label{fig:aleatoire}
	}
	\caption{Exemple de signal déterministe et de signal aléatoire.}
\end{figure}
%

\section{section name}\label{sec:section_name}



\begin{figure}
	\centering
	\subfigure[Un signal $x(t)$.]{
		\begin{tikzpicture}[samples=50]
			\draw[-stealth] (-5,0) -- (5,0) node[right] {$t$};
			\draw[-stealth] (0,-1.5) -- (0,1.5) node[above] {$x(t)$};
			\draw[thick,domain=-4:4] plot (\x,{sin(60*\x+20)});
			\draw[thick, dashed, domain=-4.5:-4] plot (\x,{sin(60*\x+20)});
			\draw[thick, dashed, domain=4:4.5] plot (\x,{sin(60*\x+20)});
		\end{tikzpicture}}
		
	\subfigure[Le peigne de Dirac $p(t)=\sum_{k} \delta(t-kT)$.]{
		\begin{tikzpicture}
			\draw[-stealth] (-5,0) -- (5,0) node[right] {$t$};
			\draw[-stealth] (0,0) -- (0,2) node[above] {$p(t)$};
			\node[above left] at (0,1) {$1$};
			\foreach \n in {-4,-3,...,4}
				\draw[-stealth,thick] (\n,0) -- (\n,1);
			\foreach \n in {-4,-3,-2,2,3,4}
				\node[below] at (\n,0) {$\n T$};
			\node[below] at (-1,0) {$-T$};
			\node[below] at (0,0) {$0$};
			\node[below] at (1,0) {$T$};
			\node at (-4.7,0.5) {$\cdots$};
			\node at (4.7,0.5) {$\cdots$};
		\end{tikzpicture}}
		
	\subfigure[Le signal échantillonné $y(t)=x(t)p(t)$.]{
		\begin{tikzpicture}[samples=50,domain=-4.5:4.5]
			\draw[-stealth] (-5,0) -- (5,0) node[right] {$t$};
			\draw[-stealth] (0,-1.5) -- (0,1.5) node[above] {$y(t)$};
			\draw[dotted] plot (\x,{sin(60*\x+20)});
			\foreach \n [evaluate=\n as \x using sin(60*\n+20)] in {-4,-3,...,4}
				\draw[-stealth,thick] (\n,0) -- (\n,\x);
			\node at (-4.7,0.5) {$\cdots$};
			\node at (4.7,0.5) {$\cdots$};
		\end{tikzpicture}}
		
	\caption{\'Echantillonnage par multiplication par un peigne de Dirac.}
	\label{fig:echantillonnage1}
\end{figure}


%
\begin{align*}
	Y(f)&=X(f) \star \frac{1}{T} \sum_{k=-\infty}^{+\infty} \delta\left(f-\frac{k}{T}\right)=\frac{1}{T}\sum_{k=-\infty}^{+\infty} X(f) \star \delta\left(f-\frac{k}{T}\right)\\
	&=\frac{1}{T}\sum_{k=-\infty}^{+\infty} X\left(f-\frac{k}{T}\right)
\end{align*}
%

\begin{figure}
	\centering
	\begin{tikzpicture}
		\fill[gray]						(0,0)												rectangle	(2,2.2);
		\fill[gray]						(0,2.8)											rectangle	(5.5,3);
		\fill[gray]						(3,0.4)											rectangle	(5.5,2.85);
		\draw[-stealth]				(0,0)												--				(6,0) node[right] {$f$};
		\draw[-stealth]				(0,0)												--				(0,3.2) node[above] {$\abs{X(f)}$};
		\draw[dotted]					(0,0.4)		node[left] {$\Delta_{2}$}	--				(3,0.4);
		\node[left]					at	(0,2.2)		{$1-\Delta_{1}$};
		\node[left]					at	(0,2.8)		{$1+\Delta_{1}$};
		\draw[thick]					(0,2.2)											--				(2,2.2)	--	(2,0) node[below] {$f_{1}$};
		\draw[thick]					(0,2.8)											--				(3,2.8)	--	(3,0.4)	--	(5.5,0.4);
		\node[below]				at	(3,0)			{$f_{2}$};
		\draw[stealth-stealth]		(-1,-1.5)										--				(5.7,-1.5);
		\draw								(2,-1.4)											--				(2,-1.6);
		\draw								(3,-1.4)											--				(3,-1.6);
		\node[left]					at	(1.8,-1)		{Bande passante};
		\node							at	(2.5,-2)		{Bande de transition};
		\node[right]				at	(3.2,-1)		{Bande coupée};
	\end{tikzpicture}
	\caption{Exemple de gabarit pour un filtre passe-bas.}
	\label{fig:gabaritFrequence}
\end{figure}










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\bibliography{TouteLaBibliographie}

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\end{document}
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