{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8f8b08b8",
   "metadata": {},
   "source": [
    "# Traitement du Signal - TDM2 : Manipulation de signaux temporels"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4924f741",
   "metadata": {},
   "source": [
    "Aujourd'hui, après une bonne introduction de NumPy la semaine dernière, on va pouvoir rentrer dans le vif du sujet, à savoir les signaux. Donc, ce n'est pas très compliqué : on va tracer beaucoup de signaux. L'idée est que vous mettiez en pratique ce que vous avez vu durant le précédent TDM, afin de construire et afficher les signaux efficacement.\n",
    "\n",
    "Après avoir vu NumPy, on va utiliser également la librairie Matplotlib, dédiée à l'affichage de données sous toute forme (courbes, graphiques, etc.). Je vous invite donc à faire un tour sur la documentation de ce package, avec évidemment la documentation de NumPy:\n",
    "- NumPy : https://numpy.org/doc/2.3/user/index.html\n",
    "- Matplotlib : https://matplotlib.org/stable/index.html"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "807a0dc8",
   "metadata": {},
   "source": [
    "---\n",
    "## Correction du TDM : préambule\n",
    "\n",
    "Pour cette correction de TDM, je vais vous donner pour chaque algorithme une version minimale attendue (c'est-à-dire ce que j'attends que vous codiez au niveau minimum) et une version optimisée. Je vous conseille dans un premier temps de vérifier vos résultats avec ceux de la correction, afin de corriger les potentielles erreurs que vous avez, mais également de jeter un coup d'oeil à la version optimisée. Certaines manipulations peuvent être complexes, mais en réalité, la plupart de celles utilisées sont à votre niveau. L'objectif est que vous puissiez vous améliorer dans votre manière de coder avec NumPy et Matplotlib, même si vous avez déjà une première base fonctionnelle."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a165c65",
   "metadata": {
    "vscode": {
     "languageId": "plaintext"
    }
   },
   "source": [
    "---\n",
    "\n",
    "## Exercice 1 : Traçons plein de signaux !\n",
    "\n",
    "Dans Traitement du Signal, il y'a Signal. On va donc partir de la base : créer des signaux via des tableaux unidimensionnels NumPy et tracer les signaux dans de jolies figures via Matplotlib. Pas de panique, on va y aller pas à pas, avec pour commencer, l'importation des librairies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9e1a5ac5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importation des librairies\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f116f4ad",
   "metadata": {},
   "source": [
    "### Axe temporel\n",
    "\n",
    "Lorsqu'on trace un signal dans le domaine temporel, on affiche l'intensité du signal en fonction du temps. On va donc d'abord créer un vecteur symbolisant le temps en secondes.\n",
    "\n",
    "Créez un tableau unidimensionnel NumPy $t$, allant de -5 à 5 secondes avec un pas de temps de 0.01 secondes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "11953449",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "# Création de l'axe temporel t\n",
    "\n",
    "# VERSION MINIMALE\n",
    "t = [] # Création d'une liste vide\n",
    "for i in range(-500,500): #i varie de -500 à 500 (on ne peut itérer que sur des entiers avec range)\n",
    "    t.append(i/100) # On ajoute chaque élément i divisé par 100 dans la liste t, pour avoir un pas de 0.01\n",
    "\n",
    "t = np.array(t) # On transforme la liste en tableau NumPy\n",
    "\n",
    "# VERSION OPTIMISEE\n",
    "t = np.arange(-5,5,0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bafd39d7",
   "metadata": {},
   "source": [
    "On a notre axe temporel, créeons maintenant notre premier signal. Il est représenté sous forme de tableau unidimensionnel de même taille que l'axe temporel. Chaque valeur du signal à l'indice $i$ correspond alors à l'intensité du signal au moment $t[i]$.\n",
    "\n",
    "Notre premier signal est simple. Créez un signal proportionnel au temps, toujours sous forme de tableau NumPy unidimensionnel : $s(t) = A \\cdot t$ avec $A=0.5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4b30a8b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "# Création du signal s\n",
    "\n",
    "# VERSION MINIMALE\n",
    "A = 0.5\n",
    "s = [] # s est initialisé comme une liste vide\n",
    "for i in range(len(t)): # On itère sur la longueur de t (0->len(t)-1)\n",
    "    s.append(t[i]*A) # On ajoute à s la valeur t[i]*A\n",
    "s = np.array(s) # On transforme la liste en tableau NumPy\n",
    "\n",
    "# VERSION OPTIMISEE\n",
    "A = 0.5\n",
    "# Ici, je multiplie directement le vecteur t par un scalaire A, ce qui nous donne un vecteur\n",
    "s = A*t"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cf82da2",
   "metadata": {},
   "source": [
    "On a notre signal, notre axe temporel, il suffit alors de tracer tout ça ! On va utiliser la fonction plot de Matplotlib ([Tutoriel](https://matplotlib.org/stable/gallery/lines_bars_and_markers/simple_plot.html#sphx-glr-gallery-lines-bars-and-markers-simple-plot-py)). Faites moi une jolie figure, avec:\n",
    "- Un titre\n",
    "- Les noms des axes (et leurs unités s'il y'en a)\n",
    "- Une légende de la courbe (on sera amené à afficher plusieurs courbes sur une seule figure, donc une légende permet de mieux comprendre à quoi correspond chaque courbe)\n",
    "\n",
    "*PS: Il y'a dans le tutoriel des fonctions qui ne sont pas utiles. Veuillez sélectionner uniquement celles qui sont pertinentes...*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2096cd0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Affichage du signal s selon l'axe temporel t\n",
    "\n",
    "# On crée la figure\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "# On trace s en ordonnée en fonction de t en abcisse\n",
    "ax.plot(t, s)\n",
    "\n",
    "# On définit le titre de la figure, ainsi que le label des axes\n",
    "ax.set(xlabel='Temps (s)', ylabel='Intensité du signal',\n",
    "       title='Signal s(t)')\n",
    "\n",
    "# On affiche la grille de fond (optionnel)\n",
    "ax.grid()\n",
    "\n",
    "# On affiche la figure\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15c1ba9d",
   "metadata": {},
   "source": [
    "Voilà, notre premier signal est tracé. A vous de jouer !"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfcbebc1",
   "metadata": {},
   "source": [
    "### Signal porte $a(t)$\n",
    "\n",
    "La fonction du signal porte est définie par l'équation suivante :\n",
    "\n",
    "\n",
    "\\begin{equation*}\n",
    "a(t) = \\Pi(t) = \n",
    "\\begin{cases} \n",
    "1, & \\text{si } |t| \\leq \\frac{1}{2}, \\\\\n",
    "0, & \\text{sinon}.\n",
    "\\end{cases}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3e3d3004",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création et affichage du signal a\n",
    "\n",
    "# VERSION MINIMALE\n",
    "a = []\n",
    "for i in range(len(t)):\n",
    "    if abs(t[i])<=0.5:\n",
    "        a.append(1)\n",
    "    else:\n",
    "        a.append(0)\n",
    "a = np.array(a)\n",
    "\n",
    "# VERSION OPTIMISEE\n",
    "a = np.where(np.abs(t)<=0.5, 1, 0)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(t,a,label=\"Signal a\")\n",
    "plt.xlabel(\"Temps (s)\")\n",
    "plt.ylabel(\"Intensité\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa851b5f",
   "metadata": {},
   "source": [
    "### Signal échelon unité $b(t)$\n",
    "\n",
    "La fonction du signal échelon unité (aussi appelée fonction de Heaviside) est définie par l'équation suivante :\n",
    "\n",
    "\\begin{equation*}\n",
    "b(t) = \\Gamma(t) = \n",
    "\\begin{cases} \n",
    "0, & \\text{si } t < 0, \\\\\n",
    "1, & \\text{si } t \\geq 0.\n",
    "\\end{cases}\n",
    "\\end{equation*}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0eea7bac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création et affichage du signal \n",
    "\n",
    "# VERSION MINIMALE\n",
    "b = []\n",
    "for i in range(len(t)):\n",
    "    if t[i]<0:\n",
    "        b.append(0)\n",
    "    else:\n",
    "        b.append(1)\n",
    "b = np.array(b)\n",
    "\n",
    "# VERSION OPTIMISEE\n",
    "b = np.where(t>=0, 1, 0)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(t,b,label=\"Signal b\")\n",
    "plt.xlabel(\"Temps (s)\")\n",
    "plt.ylabel(\"Intensité\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05bd593b",
   "metadata": {},
   "source": [
    "### Signal Échelon Retardé $c(t)$\n",
    "\n",
    "La fonction du signal échelon retardé est une version décalée dans le temps de la fonction échelon unité. Si le retard est $t_{0}$, l'équation est donnée par :\n",
    "\n",
    "\\begin{equation*}\n",
    "c(t) = \\Gamma(t - t_0) = \n",
    "\\begin{cases} \n",
    "0, & \\text{si } t < t_0, \\\\\n",
    "1, & \\text{si } t \\geq t_0.\n",
    "\\end{cases}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4be9f8e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création et affichage du signal c\n",
    "\n",
    "# VERSION MINIMALE\n",
    "t0=0.5\n",
    "c = []\n",
    "for i in range(len(t)):\n",
    "    if t[i]<t0:\n",
    "        c.append(0)\n",
    "    else:\n",
    "        c.append(1)\n",
    "c = np.array(c)\n",
    "\n",
    "# VERSION OPTIMISEE\n",
    "c = np.where(t>=t0, 1, 0)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(t,c,label=\"Signal c\")\n",
    "plt.xlabel(\"Temps (s)\")\n",
    "plt.ylabel(\"Intensité\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08947a3a",
   "metadata": {},
   "source": [
    "### Signal $d(t)$\n",
    "Le signal $d(t)$ est défini par l'équation suivante :\n",
    "\n",
    "\\begin{equation*}\n",
    "d(t)= d1(t) \\cdot d2(t) \\cdot d3(t)\n",
    "\\end{equation*}\n",
    "\n",
    "avec :\n",
    "\n",
    "\\begin{equation*}\n",
    "d1(t)= (-t + 3) \n",
    "\\end{equation*}\n",
    "\n",
    "\\begin{equation*}\n",
    "d2(t)= \\Gamma(t + 1)\n",
    "\\end{equation*}\n",
    "\n",
    "\\begin{equation*}\n",
    "d3(t)= \\Gamma(-t + 3)\n",
    "\\end{equation*}\n",
    "\n",
    "Affichez sur la même figure les signaux $d2(t)$, $d3(t)$ et $d(t)$ (n'oubliez pas les légendes !!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "792ffdcf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création et affichage du signal d\n",
    "\n",
    "# VERSION MINIMALE\n",
    "d1 = []\n",
    "for i in range(len(t)):\n",
    "    d1.append(-t[i]+3)\n",
    "d1 = np.array(d1)\n",
    "\n",
    "d2 = []\n",
    "for i in range(len(t)):\n",
    "    if t[i]+1<0:\n",
    "        d2.append(0)\n",
    "    else:\n",
    "        d2.append(1)\n",
    "d2 = np.array(d2)\n",
    "\n",
    "d3 = []\n",
    "for i in range(len(t)):\n",
    "    if -t[i]+3<0:\n",
    "        d3.append(0)\n",
    "    else:\n",
    "        d3.append(1)\n",
    "d3 = np.array(d3)\n",
    "\n",
    "d = []\n",
    "for i in range(len(t)):\n",
    "    d.append(d1[i]*d2[i]*d3[i])\n",
    "d = np.array(d)\n",
    "\n",
    "# VERSION OPTIMISEE\n",
    "d1 = -t+3\n",
    "d2 = np.where(t>=-1, 1, 0)\n",
    "d3 = np.where(t<=3, 1, 0)\n",
    "d=d1*d2*d3\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(t,d2,label=\"Signal d2\")\n",
    "plt.plot(t,d3,label=\"Signal d3\")\n",
    "plt.plot(t,d,label=\"Signal d\")\n",
    "plt.xlabel(\"Temps (s)\")\n",
    "plt.ylabel(\"Intensité\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fb92f59",
   "metadata": {},
   "source": [
    "### Signal $e(t)$\n",
    "\n",
    "Le signal $e(t)$ est défini par l'équation suivante :\n",
    "\n",
    "\\begin{equation*}\n",
    "e(t) = e^{-3t} \\cdot \\Gamma(t - 1)\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "244e1930",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création et affichage du signal e\n",
    "\n",
    "# VERSION MINIMALE\n",
    "\n",
    "import math\n",
    "\n",
    "e1 = []\n",
    "for i in range(len(t)):\n",
    "    e1.append(np.exp(-3*t[i]))\n",
    "e1 = np.array(e1)\n",
    "\n",
    "e2 = []\n",
    "for i in range(len(t)):\n",
    "    if (t[i]-1<0):\n",
    "        e2.append(0)\n",
    "    else:\n",
    "        e2.append(1)\n",
    "e2 = np.array(e2)\n",
    "\n",
    "e = []\n",
    "for i in range(len(t)):\n",
    "    e.append(e1[i]*e2[i])\n",
    "e = np.array(e)\n",
    "\n",
    "# VERSION OPTIMISEE\n",
    "e1 = np.exp(-3*t)\n",
    "e2 = np.where(t-1>=0, 1, 0)\n",
    "\n",
    "e=e1*e2\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(t,e,label=\"Signal e\")\n",
    "plt.xlabel(\"Temps (s)\")\n",
    "plt.ylabel(\"Intensité\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a4be02a",
   "metadata": {},
   "source": [
    "### Signal cosinus $f(t)$\n",
    "\n",
    "Le signal cosinus est défini par l'équation suivante :\n",
    "\n",
    "\\begin{equation*}\n",
    "f(t) = \\cos(\\omega t)\n",
    "\\end{equation*}\n",
    "\n",
    "où $\\omega$ est la pulsation angulaire en radians par seconde.\n",
    "\n",
    "Ici, on prendra $\\omega = 2.5$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0631c000",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création et affichage du signal f\n",
    "\n",
    "# VERSION MINIMALE\n",
    "omega = 2.5\n",
    "f = []\n",
    "for i in range(len(t)):\n",
    "    f.append(math.cos(t[i]*omega))\n",
    "f = np.array(f)\n",
    "\n",
    "# VERSION OPTIMALE\n",
    "omega = 2.5\n",
    "f = np.cos(omega*t)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(t,f,label=\"Signal f\")\n",
    "plt.xlabel(\"Temps (s)\")\n",
    "plt.ylabel(\"Intensité\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c4c5d25",
   "metadata": {},
   "source": [
    "Tracez maintenant ce même signal mais sur un axe temporel allant de -5 à -1 puis de 1 à 5 avec un pas de temps de 0.01 secondes.\n",
    "\n",
    "*Note 1 : Il ne faut pas de valeurs à 0 entre -1 et 1, ce qui signifie qu'il faut reconstruire un autre axe temporel t', et recréer un signal f' à partir de l'axe temporel t'.*\n",
    "\n",
    "*Note 2 : Pour créer l'axe temporel t', on peut créer deux axes temporels, puis les concatener...*\n",
    "\n",
    "*Note 3, Infinity War : Si vous tracez le signal sous forme de courbe, vous allez avoir tous vos points reliés. Il faut donc tracer le signal comme si c'était un nuage de points. Allez donc voir les options possibles dans plt.plot (paramètre fmt).*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "eb4c7815",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création de l'axe temporel t'\n",
    "\n",
    "# VERSION MINIMALE\n",
    "t_ = [] \n",
    "for i in range(-500,100): \n",
    "    t_.append(i/100) \n",
    "\n",
    "for i in range(100,500): \n",
    "    t_.append(i/100) \n",
    "\n",
    "t_ = np.array(t_) \n",
    "\n",
    "# VERSION OPTIMISEE\n",
    "t_ = np.concatenate([np.arange(-5,-1,0.01),np.arange(1,5,0.01)])\n",
    "\n",
    "# Création et affichage du signal f'\n",
    "\n",
    "# VERSION MINIMALE\n",
    "omega = 2.5\n",
    "f_ = []\n",
    "for i in range(len(t_)):\n",
    "    f_.append(math.cos(t_[i]*omega))\n",
    "f_ = np.array(f_)\n",
    "\n",
    "# VERSION OPTIMALE\n",
    "omega = 2.5\n",
    "f_ = np.cos(omega*t_)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(t_,f_,'.',label=\"Signal f'\") # On précise '.' en argument pour avoir des points affichés à chaque valeur au lieu d'une courbe. \n",
    "                                      # On aurait pu utiliser également la fonction plt.scatter\n",
    "plt.xlabel(\"Temps (s)\")\n",
    "plt.ylabel(\"Intensité\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a181f37",
   "metadata": {},
   "source": [
    "### Signal périodique $g(t)$\n",
    "\n",
    "Le signal $g(t)$ est un signal périodique en $2T$, dont la période (comprise entre $0$ et $2T$) est un signal carré $u(t)$, définie par l'équation suivante:\n",
    "\n",
    "\\begin{equation*}\n",
    "    u(t) = \\left \\{\n",
    "                \\begin{array}{ll}\n",
    "                    1, & \\text{si } 0 \\leq t \\leq T\\\\\n",
    "                    0, & \\text{si } T \\leq t \\leq 2T \\\\\n",
    "                \\end{array}\n",
    "                \\right.\n",
    "\\end{equation*}\n",
    "\n",
    "On prendra ici $T$ = 1 secondes.\n",
    "\n",
    "*Note : pour vous aider dans la construction d'un signal périodique, ici $g(t)$, voici la marche à suivre:*\n",
    "- *Créez d'abord $t'$, une représentation alternative de l'axe temporel $t$, mais indiquant la position dans la période $2T$ (c'est-à dire qu'au lieu d'avoir des valeurs variant de -5 à 5 secondes, vous aurez une répétition de variations entre $0$ et $2T$ dans notre exemple)*\n",
    "\n",
    "- *Construisez ensuite $g(t)$ non pas en fonction de $t$ mais en fonction de $t'$. De ce fait, vous aurez votre signal périodique*\n",
    "- *Lorsque vous affichez votre signal, vous tracerez $g(t)$ en fonction de $t$*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "41fb5687",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création et affichage du signal g\n",
    "\n",
    "# VERSION MINIMALE\n",
    "T = 1\n",
    "g = []\n",
    "for i in range(len(t)):\n",
    "    if (t[i]%(2*T) <= T):\n",
    "        g.append(1)\n",
    "    else:\n",
    "        g.append(0)\n",
    "g = np.array(g)\n",
    "\n",
    "# VERSION OPTIMISEE\n",
    "T = 1\n",
    "# Construction de l'axe temporel périodique t_prime\n",
    "t_prime = t%(2*T)\n",
    "\n",
    "# Construction de g(t) en fonction de t_prime\n",
    "g = np.where(t_prime<=T, 1, 0)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(t,g,label=\"Signal g\")\n",
    "plt.xlabel(\"Temps (s)\")\n",
    "plt.ylabel(\"Intensité\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55a5f6a2",
   "metadata": {},
   "source": [
    "### Signal périodique $h(t)$\n",
    "\n",
    "Allez, un dernier signal ! Le signal $h(t)$ est un signal périodique en $2T$, dont la période (comprise entre $-T$ et $T$) est un signal triangulaire $\\Delta(t)$, définie par l'équation suivante:\n",
    "\n",
    "\\begin{equation*}\n",
    "    \\Delta(t) = \\left \\{\n",
    "                \\begin{array}{ll}\n",
    "                    t+T, & \\text{si } -T \\leq t \\leq 0 \\\\\n",
    "                    -t+T, & \\text{si } 0 \\leq t \\leq T \\\\\n",
    "                \\end{array}\n",
    "                \\right.\n",
    "\\end{equation*}\n",
    "\n",
    "On prendra ici $T$ = 1 secondes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "144565d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création et affichage du signal h\n",
    "\n",
    "T = 1\n",
    "\n",
    "# Construction de l'axe temporel périodique t_prime\n",
    "t_prime = (t+T)%(2*T)-T\n",
    "\n",
    "# Construction de h(t) en fonction de t_prime\n",
    "h = np.where(t_prime<=0, t_prime+T, T-t_prime)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(t,h,label=\"Signal h\")\n",
    "plt.xlabel(\"Temps (s)\")\n",
    "plt.ylabel(\"Intensité\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32cd29fe",
   "metadata": {},
   "source": [
    "### Une jolie figure qui regroupe tous les signaux !\n",
    "\n",
    "Affichez maintenant tous les signaux ($a$, $b$, $c$, $d$, $e$, $f$, $g$ et $g$) dans une seule figure divisées en 8 sous-figures avec la fonction subplot sur Matplotlib ([Tutoriel](https://matplotlib.org/stable/gallery/subplots_axes_and_figures/subplots_demo.html)). N'oubliez pas les titres/sous-titres. L'objectif est de faire une figure lisible, donc n'hésitez pas à regarder en détail la documentation Matplotlib !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "38324f5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Affichage des 8 signaux sur une même figure\n",
    "plt.subplots(4,2)\n",
    "\n",
    "plt.subplot(421)\n",
    "plt.plot(t,a)\n",
    "plt.title(\"Signal a\")\n",
    "\n",
    "plt.subplot(422)\n",
    "plt.plot(t,b)\n",
    "plt.title(\"Signal b\")\n",
    "\n",
    "plt.subplot(423)\n",
    "plt.plot(t,c)\n",
    "plt.title(\"Signal c\")\n",
    "\n",
    "plt.subplot(424)\n",
    "plt.plot(t,d)\n",
    "plt.title(\"Signal d\")\n",
    "\n",
    "plt.subplot(425)\n",
    "plt.plot(t,e)\n",
    "plt.title(\"Signal e\")\n",
    "\n",
    "plt.subplot(426)\n",
    "plt.plot(t,f)\n",
    "plt.title(\"Signal f\")\n",
    "\n",
    "plt.subplot(427)\n",
    "plt.plot(t,g)\n",
    "plt.title(\"Signal g\")\n",
    "\n",
    "plt.subplot(428)\n",
    "plt.plot(t,h)\n",
    "plt.title(\"Signal h\")\n",
    "\n",
    "# Fonction super utile qui réajuste automatiquement la figure pour que tous les labels et signaux soient bien visibles\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e9c407e",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Exercice 2 (optionnel) : Des signaux de détresse !\n",
    "\n",
    "Si vous en êtes là, c'est que vous avez bien tracé les précédents signaux. Le challenge va devenir plus difficile. On va maintenant tracer PLEIN de signaux particuliers, mais pour un but précis que vous devinerez à la fin...\n",
    "\n",
    "*Note : pour un meilleur rendu, je vous conseille de tracer les différents signaux sous forme de nuages de points (comme la fonction $f'$ vue précédemment), à la différence des courbes. C'est seulement pour cet exercice...*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76335706",
   "metadata": {},
   "source": [
    "### Signal B1\n",
    "\n",
    "1er signal à construire : \n",
    "- L'axe temporel T1 est défini de -0.45 à 0.45, avec un pas de 0.005\n",
    "- Le signal B1 suit l'équation suivante:\n",
    "\n",
    "\\begin{equation*}\n",
    "    B1(t) = 2\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ffa7d17f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création de l'axe temporel T1\n",
    "T1 = np.arange(-0.45, 0.45, 0.005)\n",
    "\n",
    "# Création du signal B1\n",
    "B1 = np.ones_like(T1)*2\n",
    "\n",
    "# Affichage du signal B1 selon l'axe temporel T1\n",
    "plt.figure()\n",
    "plt.plot(T1,B1,'.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "529ce5b3",
   "metadata": {},
   "source": [
    "### Signal B2\n",
    "\n",
    "2ème signal à construire : \n",
    "- L'axe temporel T2 est défini de -7 à -3, puis de 3 à 7, avec un pas de 0.001\n",
    "- Le signal B2 suit l'équation suivante:\n",
    "\n",
    "\\begin{equation*}\n",
    "    B2(t) = 3\\sqrt{-\\left(\\frac{t}{7}\\right)^{2}+1}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b70c8958",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création de l'axe temporel T2\n",
    "T2 = np.concatenate([np.arange(-7, -3, 0.001), np.arange(3, 7, 0.001)])\n",
    "\n",
    "# Création du signal B2\n",
    "B2 = 3*np.sqrt(-(T2/7)**2+1)\n",
    "\n",
    "# Affichage du signal B2 selon l'axe temporel T2\n",
    "plt.figure()\n",
    "plt.plot(T2,B2,'.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e043af1c",
   "metadata": {},
   "source": [
    "### Signal B3\n",
    "\n",
    "3ème signal à construire : \n",
    "- L'axe temporel T3 est défini de -7 à -4, puis de 4 à 7, avec un pas de 0.001\n",
    "- Le signal B3 suit l'équation suivante:\n",
    "\n",
    "\\begin{equation*}\n",
    "    B3(t) = -3\\sqrt{-\\left(\\frac{t}{7}\\right)^{2}+1}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "6f447d7a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création de l'axe temporel T3\n",
    "T3 = np.concatenate([np.arange(-7, -4, 0.001), np.arange(4, 7, 0.001)])\n",
    "\n",
    "# Création du signal B3\n",
    "B3 = -3*np.sqrt(-(T3/7)**2+1)\n",
    "\n",
    "# Affichage du signal B3 selon l'axe temporel T3\n",
    "plt.figure()\n",
    "plt.plot(T3,B3,'.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "758958a3",
   "metadata": {},
   "source": [
    "### Signal B4\n",
    "\n",
    "4ème signal à construire : \n",
    "- L'axe temporel T4 est défini par $0.75 \\leq |t| \\leq 1$, avec un pas de 0.001\n",
    "- Le signal B4 suit l'équation suivante:\n",
    "\n",
    "\\begin{equation*}\n",
    "    B4(t) = 9-8\\left|t\\right|\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3cf259cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création de l'axe temporel T4\n",
    "T4 = np.concatenate([np.arange(-1, -0.75, 0.001), np.arange(0.75, 1, 0.001)])\n",
    "\n",
    "# Création du signal B4\n",
    "B4 = 9-8*np.abs(T4)\n",
    "\n",
    "# Affichage du signal B4 selon l'axe temporel T4\n",
    "plt.figure()\n",
    "plt.plot(T4,B4,'.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96479dac",
   "metadata": {},
   "source": [
    "### Signal B5\n",
    "\n",
    "5ème signal à construire : \n",
    "- L'axe temporel T5 est défini par $0.45 \\leq |t| \\leq 0.75$, avec un pas de 0.001\n",
    "- Le signal B5 suit l'équation suivante:\n",
    "\n",
    "\\begin{equation*}\n",
    "    B5(t) = 3\\left|t\\right|+0.75\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6aa9dfb8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création de l'axe temporel T5\n",
    "T5 = np.concatenate([np.arange(-0.75, -0.45, 0.001), np.arange(0.45, 0.75, 0.001)])\n",
    "\n",
    "# Création du signal B5\n",
    "B5 = 3*np.abs(T5)+0.75\n",
    "\n",
    "# Affichage du signal B5 selon l'axe temporel T5\n",
    "plt.figure()\n",
    "plt.plot(T5,B5,'.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8252a7c0",
   "metadata": {},
   "source": [
    "### Signal B6\n",
    "\n",
    "6ème signal à construire : \n",
    "- L'axe temporel T6 est défini par $1 \\leq |t| \\leq 3$, avec un pas de 0.001\n",
    "- Le signal B6 suit l'équation suivante:\n",
    "\n",
    "\\begin{equation*}\n",
    "    B6(t) = 1.5-.5\\left|x\\right|-\\frac{6\\sqrt{10}}{14}\\left(\\sqrt{3-x^{2}+2\\left|x\\right|}-2\\right)\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e0cc2020",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création de l'axe temporel T6\n",
    "T6 = np.concatenate([np.arange(-3,-1, 0.001), np.arange(1, 3, 0.001)])\n",
    "\n",
    "# Création du signal B6\n",
    "B6 = 1.5 - 0.5*abs(T6) - (6*np.sqrt(10)/14)*(np.sqrt(3-T6**2+2*abs(T6))-2)\n",
    "\n",
    "# Affichage du signal B6 selon l'axe temporel T6\n",
    "plt.figure()\n",
    "plt.plot(T6,B6,'.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c68844bc",
   "metadata": {},
   "source": [
    "### Signal B7\n",
    "\n",
    "7ème signal à construire : \n",
    "- L'axe temporel T7 est défini de -4 à 4, avec un pas de 0.0001\n",
    "- Le signal B7 suit l'équation suivante:\n",
    "\n",
    "\\begin{equation*}\n",
    "    B7(t) = \\left|\\frac{t}{2}\\right|-\\frac{3\\sqrt{33}-7}{112}t^{2}+\\sqrt{1-\\left(\\operatorname{abs}\\left(\\left|t\\right|-2\\right)-1\\right)^{2}}-3\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "b7d61209",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création de l'axe temporel T7\n",
    "T7 = np.arange(-4, 4, 0.0001)\n",
    "\n",
    "# Création du signal B7\n",
    "B7 = abs(T7/2) - ((3*np.sqrt(33)-7)/112)*T7**2 + np.sqrt(1-(abs(abs(T7)-2)-1)**2) -3\n",
    "\n",
    "# Affichage du signal B7 selon l'axe temporel T7\n",
    "plt.figure()\n",
    "plt.plot(T7,B7,'.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d60e64ec",
   "metadata": {},
   "source": [
    "### Le reveal final\n",
    "\n",
    "Il est temps de tracer les 7 signaux avec leur axes temporels respectifs sur une seule et même figure. Créez donc cette figure mystérieuse, avec les courbes/nuages de points en noir pour un effet plus dramatique...\n",
    "\n",
    "Et répondez à la question que tout le monde se pose : qui devrait débarquer après avoir tracer ces 7 signaux ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "d4964b8a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Affichage des 7 signaux construits sur une seule et même figure\n",
    "plt.figure()\n",
    "plt.plot(T1,B1,'k.')\n",
    "plt.plot(T2,B2,'k.')\n",
    "plt.plot(T3,B3,'k.')\n",
    "plt.plot(T4,B4,'k.')\n",
    "plt.plot(T5,B5,'k.')\n",
    "plt.plot(T6,B6,'k.')\n",
    "plt.plot(T7,B7,'k.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "accb32d1",
   "metadata": {},
   "source": [
    "**_REPONSE :_** TANANANANANANANANA BATMAN !!!!!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b7b2cfb",
   "metadata": {},
   "source": [
    "## Rendu de TP\n",
    "Le rendu qui vous est demandé pour les TP de TIM est la version HTML de ce notebook. Pour cela, avant de déposer votre rendu, vous devez :\n",
    "- Redémarrer le noyau/kernel Python en effaçant les sorties\n",
    "- Exécuter toutes les cellules du Notebook à la suite\n",
    "- Exporter le fichier en HTML"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "deep",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
