{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8f8b08b8",
   "metadata": {},
   "source": [
    "# Traitement du Signal - TP1 : Manipulation de signaux temporels\n",
    "\n",
    "---\n",
    "**AVANT DE COMMENCER, TRES IMPORTANT !!**\n",
    "\n",
    "Durant ce semestre, vous aurez des TPs à rendre.\n",
    "\n",
    "Vous aurez donc dans ces fichiers de TPs des cellules de codes à compléter, comme celle-ci :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c59a17ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4dd33748",
   "metadata": {},
   "source": [
    "Ou des cellules texte à compléter (commençant par **_REPONSE_**) :"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae067911",
   "metadata": {},
   "source": [
    "**_REPONSE :_** _Ici, vous écrivez votre réponse._"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a77b0aff",
   "metadata": {},
   "source": [
    "Vérifiez bien avant de rendre un TP que toutes les cellules (codes et texte) soient bien **complétées**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4924f741",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "L'objectif de ce premier TP va être de prendre en main les packages python NumPy et Matplotlib pour tracer des signaux. Ces deux librairies sont essentielles et vont être utilisées durant tout le semestre, donc prenez bien le temps de lire la documentation :\n",
    "- NumPy : https://numpy.org/doc/2.3/user/index.html\n",
    "- Matplotlib : https://matplotlib.org/stable/index.html\n",
    "\n",
    "\n",
    "Je vous recommande **FORTEMENT** :\n",
    "- de prendre des notes durant les TP, sur les fonctions que vous utilisez, comme sur les résultats obtenus\n",
    "- de vous partager le clavier si vous êtes en binôme ! Il faut que tout le monde code !\n",
    "- de ne pas utiliser ChatGPT ou tout autre IA. Vous aurez un examen pratique sans possibilité de les consulter, donc autant apprendre en TP"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "807a0dc8",
   "metadata": {},
   "source": [
    "---\n",
    "## Correction du TP : préambule\n",
    "\n",
    "Pour cette correction de TP, 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",
    "## Partie 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": 2,
   "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": 3,
   "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": 4,
   "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 titre, noms des axes, légende, etc.\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": 5,
   "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",
    "\\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": 6,
   "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.zeros_like(t)\n",
    "a[np.abs(t)<=0.5]=1\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",
    "\\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": 7,
   "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.zeros_like(t)\n",
    "b[t>=0]=1\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",
    "\\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": 8,
   "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",
    "t0=0.5\n",
    "c = np.zeros_like(t)\n",
    "c[t>=t0]=1\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": 9,
   "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.zeros_like(t)\n",
    "d2[t>=-1]=1\n",
    "d3 = np.zeros_like(t)\n",
    "d3[t<=3]=1\n",
    "\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": 10,
   "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.zeros_like(t)\n",
    "e2[t-1>=0]=1\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",
    "y(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": 11,
   "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": 12,
   "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), périodique en T, est défini par l'équation suivante:\n",
    "\n",
    "\\begin{equation*}\n",
    "    g(t) = \\left \\{\n",
    "            \\begin{array}{ll}\n",
    "                t & 0 \\leq t \\leq \\frac{T}{2}\\\\\n",
    "                -t+T & \\frac{T}{2} \\leq t \\leq T \\\\\n",
    "            \\end{array}\n",
    "            \\right.\n",
    "\\end{equation*}\n",
    "\n",
    "On prendra ici T = 2 secondes.\n",
    "\n",
    "*Note : Pour vous faciliter le travail, créez d'abord un vecteur qui représente l'axe temporel modulo la période. Vous saurez ainsi à chaque instant t où vous en êtes dans la période T.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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 = 2\n",
    "g = []\n",
    "for i in range(len(t)):\n",
    "    if (t[i]%T<=T/2):\n",
    "        g.append(t[i]%T)\n",
    "    else:\n",
    "        g.append(-(t[i]%T)+T)\n",
    "g = np.array(g)\n",
    "\n",
    "# VERSION OPTIMISEE\n",
    "T = 2\n",
    "t_modulo_T = t%T\n",
    "g = t_modulo_T\n",
    "# Ici, j'utilise un masque, c'est-à-dire que je sélectionne les valeurs de mon vecteur en fonction d'une condition, et je peux ensuite les modifier\n",
    "g[t_modulo_T>=T/2] = -g[t_modulo_T>=T/2]+T\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": "32cd29fe",
   "metadata": {},
   "source": [
    "### Une jolie figure qui regroupe tous les signaux !\n",
    "\n",
    "Affichez maintenant tous les signaux ($a$, $b$, $c$, $d$, $e$, $f$, $f'$ 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_,f_,'.')\n",
    "plt.title(\"Signal f'\")\n",
    "\n",
    "plt.subplot(428)\n",
    "plt.plot(t,g)\n",
    "plt.title(\"Signal g\")\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",
    "## Partie 2 : Vous savez tracer des signaux ? Ok !\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..."
   ]
  },
  {
   "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": "TIM",
   "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": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
