{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "de91e174",
   "metadata": {},
   "source": [
    "# Traitement du Signal - Examen blanc : Partie Manipulation\n",
    "\n",
    "## Préambule de l'examen blanc\n",
    "\n",
    "L'examen pratique sera divisé en 2 parties, sur **2 Notebooks différents** :\n",
    "- Un exercice de manipulation : un exercice pas à pas où vous devez juste appliquer ce qu'on vous demande, et qui reprend une bonne partie de ce que vous avez vu durant les précédents TPs.\n",
    "- Un exercice de réflexion : un exercice où vous avez une problématique décrite, et c'est à vous de proposer et de justifier les bons outils permettant d'atteindre l'objectif demandé, tout en faisant une analyse critique de vos résultats obtenus.\n",
    "\n",
    "Avec ces deux exercices, vous avez quelques ressources supplémentaires :\n",
    "- un fichier *utils.py*, avec des fonctions développées durant les TPs qui ne sont pas disponibles dans les packages NumPy ou SciPy\n",
    "- un fichier *index* qui recense tous les noms des fonctions NumPy/SciPy que nous avons utilisé durant les précédents TPs (sans précision cependant sur leur fonctionnement)\n",
    "- Les documentations *Python / NumPy / Scipy / Matplotlib* disponibles via Firefox\n",
    "\n",
    "Chacun des notebooks de cet examen blanc décrira les modalités d'évaluations de chacune des parties"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "627a7516",
   "metadata": {},
   "source": [
    "## Préambule de l'exercice de manipulation\n",
    "\n",
    "L'exercice de manipulation a pour objectif d'évaluer vos capacités techniques en TDS (maîtrise en Python/NumPy/Matplotlib, connaissances des bases de TDS). Chaque manipulation demandée se fait pas à pas. A certains endroits, vous aurez :\n",
    "- des checkups : des cellules déjà écrites vérifiant que le résultat obtenu est correct (via la comparaison avec le résultat que vous devriez théoriquement obtenir)\n",
    "- des backups : des cellules permettant de charger le résultat que vous devriez normalement avoir, pour qu'un échec sur une question n'affecte pas la suite de l'exercice\n",
    "\n",
    "Les questions demandées ne sont globalement pas compliquées (vous avez déjà vu tout ce qui sera demandé durant le semestre en TP), mais le correcteur aura une vigilance accrue sur la **précision** des résultats obtenus/affichés. \n",
    "\n",
    "*Exemple: lorsque vous affichez un signal, si l'axe temporel/fréquentiel n'est pas défini en abcisses, vous perdrez bêtement des points*\n",
    "\n",
    "Vous n'avez pas besoin d'utiliser les fonctions disponibles dans le fichier *utils.py*.\n",
    "\n",
    "A vous de jouer, bon courage :D"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba61ec29",
   "metadata": {},
   "source": [
    "## Exercice de manipulation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6387966",
   "metadata": {},
   "source": [
    "**0)** Chargez les libraries nécessaires pour cet exercice : *NumPy* (**np**), *Scipy* et le sous-package *Pyplot* de *Matplotlib* (**plt**)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "72ad45ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "# Chargement des librairies Numpy (np), Scipy et Pyplot de Matplotlib (plt)\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import scipy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42ae01a9",
   "metadata": {},
   "source": [
    "**1)** Construisez un signal carré défini de la manière suivante:\n",
    "\n",
    "\\begin{equation*}\n",
    "    s(t) = \\begin{cases}\n",
    "                1 & \\text{si t} \\in [0,1[\\\\\n",
    "                0 & \\text{si t} \\in [1,2]\n",
    "                \\end{cases}\n",
    "\\end{equation*}\n",
    "\n",
    "Le signal sera défini pour $t$ allant de 0 à 2 secondes, avec un temps d'échantillonnage $T_e = 0.02$ secondes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "21b03658",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "# Création du signal carré\n",
    "\n",
    "Te = 0.02 # Temps d'échantillonnage\n",
    "T = 2 # Durée du signal en secondes\n",
    "\n",
    "t_s = np.arange(0,T,Te) # Axe temporel du signal carré\n",
    "s = np.concatenate([np.ones(len(t_s)//2),np.zeros(len(t_s)//2)])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d1dec5e",
   "metadata": {},
   "source": [
    "Affichez le signal $s(t)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7c1d65f3",
   "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(t)\n",
    "plt.figure()\n",
    "plt.plot(t_s,s)\n",
    "plt.title(\"Signal s(t)\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e920d3a",
   "metadata": {},
   "source": [
    "**CHECKUP 1**\n",
    "\n",
    "**Exécutez la cellule ci-dessous pour vérifier votre résultat précédent**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fc246223",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checkup 1 validé\n"
     ]
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# CHECKUP 1\n",
    "\n",
    "def check_array_equal(a,b,signal_name):\n",
    "    # Vérification des tailles\n",
    "    assert a.shape == b.shape, (\n",
    "        f\"Erreur : {signal_name} n'est pas de la bonne taille \"\n",
    "        f\"{a.shape} != {b.shape}\"\n",
    "    )\n",
    "    # Vérification des valeurs\n",
    "    \n",
    "    assert np.allclose(a, b,1e-8), (f\"Erreur : {signal_name} est incorrect :\\n\"\n",
    "                                f\"Ce que vous devriez obtenir : {b}\\n\"\n",
    "                                f\"Votre signal : {a}\\n\")\n",
    "\n",
    "# Mettez ici vos variables correspondant au signal et à son axe temporel\n",
    "s = s # Signal s(t)\n",
    "t_s = t_s # Axe temporel de s(t)\n",
    "\n",
    "backup_1_s = np.load(\"backup/1_s.npy\")\n",
    "backup_1_t_s = np.load(\"backup/1_t_s.npy\")\n",
    "\n",
    "check_array_equal(s,backup_1_s,\"le signal s\")\n",
    "check_array_equal(t_s,backup_1_t_s,\"l'axe temporel de s\")\n",
    "\n",
    "print(\"Checkup 1 validé\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc2752ae",
   "metadata": {},
   "source": [
    "**BACKUP 1**\n",
    "\n",
    "**Décommentez et exécutez la cellule ci-dessous si vous n'avez pas validez la cellule précédente**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f7a069b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# BACKUP 1\n",
    "#s = np.load(\"backup/1_s.npy\")\n",
    "#t_s = np.load(\"backup/1_t_s.npy\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e720f08",
   "metadata": {},
   "source": [
    "**2)** Créez le signal *h(t)*, une réponse impulsionnelle qui permettra ensuite de calculer $x(t) = s(t) \\ast h(t)$ tel que $x(t)$ soit un signal périodique évoluant durant 10 secondes avec une période de $s(t)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "17c16d4b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "# Création de h(t)\n",
    "\n",
    "t_h = np.arange(0,10,Te) # Axe temporel de h\n",
    "h = np.where(t_h%T==0, 1, 0) # Création de h"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74765fce",
   "metadata": {},
   "source": [
    "Affichez le signal $h(t)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "290f192b",
   "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 de h(t)\n",
    "plt.figure()\n",
    "plt.plot(t_h,h)\n",
    "plt.title(\"Signal h(t)\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43964cb8",
   "metadata": {},
   "source": [
    "**3)** Calculez maintenant $x(t) = s(t) \\ast h(t)$, ainsi que son axe temporel\n",
    "\n",
    "*Note : modifiez également x(t) afin qu'il évolue bien entre 0 et 10 secondes*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f800dcd9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "# Calcul de x(t)\n",
    "x = np.convolve(s,h,'full')\n",
    "# Ici, x(t) évolue sur 12 secondes (durée de s + durée de h)\n",
    "# Pour s'assurer que x(t) évolue durant 10 secondes, on le coupe pour qu'il ait la même longueur que h(t) qui évolue lui durant 10 secondes\n",
    "x = x[:len(h)]\n",
    "\n",
    "t_x = t_h # Axe temporel de x, qui est le même que celui de h\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "595d22db",
   "metadata": {},
   "source": [
    "Affichez le signal $x(t)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "be080b49",
   "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 de x(t)\n",
    "plt.figure()\n",
    "plt.plot(t_x,x)\n",
    "plt.title(\"Signal x(t)\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c488f51",
   "metadata": {},
   "source": [
    "**CHECKUP 2**\n",
    "\n",
    "**Exécutez la cellule ci-dessous pour vérifier votre résultat précédent**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4c1eb2ec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checkup 2 validé\n"
     ]
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# CHECKUP 2\n",
    "\n",
    "# Mettez ici vos variables correspondant au signal et à son axe temporel\n",
    "x = x # Signal x(t)\n",
    "t_x = t_x # Axe temporel de x(t)\n",
    "\n",
    "backup_2_x = np.load(\"backup/2_x.npy\")\n",
    "backup_2_t_x = np.load(\"backup/2_t_x.npy\")\n",
    "\n",
    "check_array_equal(x,backup_2_x,\"le signal x\")\n",
    "check_array_equal(t_x,backup_2_t_x,\"l'axe temporel de x\")\n",
    "\n",
    "print(\"Checkup 2 validé\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34baaaca",
   "metadata": {},
   "source": [
    "**BACKUP 2**\n",
    "\n",
    "**Décommentez et exécutez la cellule ci-dessous si vous n'avez pas validez la cellule précédente**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "06aa918d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# BACKUP 2\n",
    "#x = np.load(\"backup/2_x.npy\")\n",
    "#t_x = np.load(\"backup/2_t_x.npy\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94f0ef3e",
   "metadata": {},
   "source": [
    "**4)** Calculez $X(f)$, la transformée de Fourier réelle de $x(t)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e6f08031",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "# Transformée de Fourier réelle de x(t)\n",
    "X = np.fft.rfft(x)\n",
    "freq_X = np.fft.rfftfreq(len(x),Te)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d71fb2d",
   "metadata": {},
   "source": [
    "Affichez le spectre d'amplitude de $X(f)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a3c1d56c",
   "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 du spectre d'amplitude de X(f)\n",
    "amplitude_X = np.abs(X) * 2 / len(x) # Amplitude NORMALISEE de X(f)\n",
    "\n",
    "plt.figure()\n",
    "plt.stem(freq_X,amplitude_X,markerfmt=' ')\n",
    "plt.title(\"Spectre d'amplitude X(f)\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1aa1803",
   "metadata": {},
   "source": [
    "**5)** Effectuez un filtre passe-bas idéal sur $X(f)$ avec une fréquence de coupure $f_c$ = 15 Hz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "82f697e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "# Filtre passe-bas idéal de X(f)\n",
    "fc=15\n",
    "X[freq_X>fc]=0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf23737a",
   "metadata": {},
   "source": [
    "Affichez le spectre d'amplitude après application du filtre passe-bas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fb1d7291",
   "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 du spectre d'amplitude après application du filtre passe-bas\n",
    "amplitude_X = np.abs(X) * 2 / len(x) # Amplitude NORMALISEE de X(f)\n",
    "\n",
    "plt.figure()\n",
    "plt.stem(freq_X,amplitude_X,markerfmt=' ')\n",
    "plt.title(\"Spectre d'amplitude X(f) filtré\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca37d0c7",
   "metadata": {},
   "source": [
    "**6)** Modifiez $X(f)$ afin que la fréquence d'échantillonnage du signal $f_e$ = 40 Hz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "d253f40b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "# Modification de X(f) afin d'avoir une fréquence d'échantillonnage de 40 Hz\n",
    "\n",
    "# Pour avoir une fréquence d'échantillonnage de 40 Hz, \n",
    "# il suffit de couper X(f), qui évolue initialement de 0 à 25 Hz, pour qu'il ait une fréquence max \n",
    "# sur l'axe fréquentiel de 20 Hz (= fe/2)\n",
    "fe = 40\n",
    "\n",
    "indice_fe = np.argwhere(freq_X==40/2)[0][0] # On récupère l'indice du tableau où freq_X = fe\n",
    "X = X[:indice_fe+1]\n",
    "freq_X = freq_X[:indice_fe+1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c38f260c",
   "metadata": {},
   "source": [
    "Affichez le spectre d'amplitude après ré-échantillonnage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a14cf51c",
   "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 du spectre d'amplitude après ré-échantillonnage\n",
    "amplitude_X = np.abs(X) * 2 / len(x) # Amplitude NORMALISEE de X(f)\n",
    "\n",
    "plt.figure()\n",
    "plt.stem(freq_X,amplitude_X,markerfmt=' ')\n",
    "plt.title(\"Spectre d'amplitude X(f) filtré, échantillonné à 40 Hz\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03b3b859",
   "metadata": {},
   "source": [
    "**7)** Effectuez la transformée de Fourier réelle inverse pour obtenir votre nouveau signal $x(t)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "baffaa49",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "# Transformée de Fourier réelle inverse de X(f)\n",
    "x = np.fft.irfft(X)\n",
    "t_x = np.arange(0,len(x)/fe, 1/fe)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df408d96",
   "metadata": {},
   "source": [
    "Affichez le nouveau signal $x(t)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "49bd1df7",
   "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 de x(t)\n",
    "plt.figure()\n",
    "plt.plot(t_x,x)\n",
    "plt.title(\"Signal x(t) après filtrage et ré-échantillonnage\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfa002b5",
   "metadata": {},
   "source": [
    "**CHECKUP 3**\n",
    "\n",
    "**Exécutez la cellule ci-dessous pour vérifier votre résultat précédent**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "713cd0cb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checkup 3 validé\n"
     ]
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# CHECKUP 3\n",
    "\n",
    "# Mettez ici vos variables correspondant au signal et à son axe temporel\n",
    "x = x # Signal x(t)\n",
    "t_x = t_x # Axe temporel de x(t)\n",
    "\n",
    "backup_3_x = np.load(\"backup/3_x.npy\")\n",
    "backup_3_t_x = np.load(\"backup/3_t_x.npy\")\n",
    "\n",
    "check_array_equal(x,backup_3_x,\"le signal x\")\n",
    "check_array_equal(t_x,backup_3_t_x,\"l'axe temporel de x\")\n",
    "\n",
    "print(\"Checkup 3 validé\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a447d5d1",
   "metadata": {},
   "source": [
    "**BACKUP 3**\n",
    "\n",
    "**Décommentez et exécutez la cellule ci-dessous si vous n'avez pas validez la cellule précédente**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "6b19f172",
   "metadata": {},
   "outputs": [],
   "source": [
    "# BACKUP 3\n",
    "#x = np.load(\"backup/3_x.npy\")\n",
    "#t_x = np.load(\"backup/3_t_x.npy\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce708ca8",
   "metadata": {},
   "source": [
    "**8)** Créez un filtre de Butterworth passe-haut d'ordre 15 avec $f_{c}$ = 5 Hz et affichez les coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "856c833a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients a : [ 1.00000000e+00 -7.49129567e+00  2.73120809e+01 -6.37925508e+01\n",
      "  1.06212361e+02 -1.33033789e+02  1.29126405e+02 -9.86764094e+01\n",
      "  5.97453495e+01 -2.86158833e+01  1.07394942e+01 -3.09788443e+00\n",
      "  6.64188241e-01 -9.98334271e-02  9.39948396e-03 -4.17593293e-04]\n",
      "Coefficients b : [ 2.04350995e-02 -3.06526493e-01  2.14568545e+00 -9.29797028e+00\n",
      "  2.78939109e+01 -6.13666039e+01  1.02277673e+02 -1.31499865e+02\n",
      "  1.31499865e+02 -1.02277673e+02  6.13666039e+01 -2.78939109e+01\n",
      "  9.29797028e+00 -2.14568545e+00  3.06526493e-01 -2.04350995e-02]\n"
     ]
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création d'un filtre de Butterworth passe-haut\n",
    "fc = 5\n",
    "order = 15\n",
    "b,a = scipy.signal.butter(order,fc,'highpass',fs=40)\n",
    "print(f\"Coefficients a : {a}\")\n",
    "print(f\"Coefficients b : {b}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "942b78ab",
   "metadata": {},
   "source": [
    "Appliquez le filtre de Butterworth créé sur le signal $x(t)$ avec la fonction *scipy.signal.lfilter*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "b61a4c10",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "# Application du filtre de Butterworth sur x(t)\n",
    "from scipy.signal import lfilter\n",
    "y = lfilter(b,a,x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fc1b1d1",
   "metadata": {},
   "source": [
    "Affichez le signal filtré"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "5ba613f6",
   "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 du signal filtré\n",
    "plt.figure()\n",
    "plt.plot(t_x,y)\n",
    "plt.title(\"Signal y(t)\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "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
}
