{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "096609fe",
   "metadata": {},
   "source": [
    "# Traitement du Signal - TP7 : Transformée de Fourier Directe\n",
    "\n",
    "La transformée de Fourier, c'est bon, vous connaissez. Mais vous savez également qu'entre l'analogique et le numérique, il y'a de sacrés différences. Ici, on va reprendre le principe de transformée de Fourier, mais celle appliquée au numérique, à savoir la **transformée de Fourier discrète (TFD)**. On va d'abord commencer par la recoder, puis comprendre l'impact du paramétrage des signaux d'entrée sur le résultat en fréquentiel et inversement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e72cde10",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "# Import des librairies\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1273ded",
   "metadata": {},
   "source": [
    "## Exercice 1 : Codage"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc1e81e9",
   "metadata": {},
   "source": [
    "Avant de faire plein de transformées, on va d'abord coder la fonction. Pour rappel, la formule de la transformée de Fourier directe est :\n",
    "\n",
    "\\begin{equation*}\n",
    "    X[k]= \\sum_{n=0}^{N-1} x[n] e^{-j2π \\frac{k}{L} n}\n",
    "\\end{equation*}\n",
    "\n",
    "Avec :\n",
    "- $N$ : Le nombre de points temporels\n",
    "- $n$ : La variable temporelle $\\in [0, N-1]$\n",
    "- $L$ : Le nombre de points fréquentiels\n",
    "- $k$ : La variable fréquentielle $\\in [0, L-1]$\n",
    "\n",
    "Vous pouvez constater ici que la longueur du signal fréquentiel $L est distincte de la longueur du signal temporel $N$. Cela veut dire qu'on peut définir $L \\neq N$ (vous verrez l'utilité plus tard). On a alors 3 cas de figures:\n",
    "- $L=N$ : le plus simple, aucune modification n'est à apporter sur le signal d'entrée\n",
    "- $L<N$ : on coupe le signal d'entrée en ne gardant que les $L$ premières valeurs\n",
    "- $L>N$ : on agrandit le signal d'entrée en rajoutant des zéros à la fin, afin qu'il soit de taille $L$.\n",
    "\n",
    "Développez la fonction de transformée de Fourier directe, prenant donc en entrée le signal et $L$ la taille  du signal fréquentiel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "68a51a0d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "\n",
    "# Fonction de padding (similaire à celle du TP2, mais modifiée pour tronquer le signal si M<len(signal))\n",
    "def padding(signal,M):\n",
    "    \"\"\"\n",
    "    Fonction de padding du signal pour l'agrandir à la taille M (si M supérieur à len(signal))\n",
    "    signal : tableau 1D Numpy, représentant un signal\n",
    "    M : entier, représentat la taille de padding attendue pour M\n",
    "    \"\"\"\n",
    "    if M==len(signal): # Même longueur\n",
    "        return signal\n",
    "    elif M<len(signal): # M inférieur à la longueur du signal\n",
    "        return signal[:M]\n",
    "    # M supérieur à la longueur du signal\n",
    "    out = np.zeros((M),dtype=signal.dtype)\n",
    "    out[:len(signal)] = signal\n",
    "    return out\n",
    "\n",
    "# Fonction de transformée de Fourier directe\n",
    "def TFD(x,L):\n",
    "    x_pad = padding(x,L)\n",
    "    X = np.zeros((L),dtype=complex)\n",
    "    for k in range(L):\n",
    "        sum_x = 0\n",
    "        for n in range(L):\n",
    "            sum_x += x_pad[n] * np.exp(-2*np.pi*k*n/L*1j)\n",
    "        X[k] = sum_x\n",
    "    return X\n",
    "\n",
    "# Une version un peu plus optimisée\n",
    "def TFD(x,L):\n",
    "    x_pad = padding(x,L)\n",
    "    n = np.arange(L) # On calcule un vecteur range de L, histoire d'éviter une boucle supplémentaire et donc d'accélerer le calcul\n",
    "    X = np.zeros((L), dtype=complex)\n",
    "    for k in range(L):\n",
    "        X[k] = (x_pad*np.exp(-2*np.pi*k*n/L*1j)).sum()\n",
    "    return X"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed7550a2",
   "metadata": {},
   "source": [
    "3 tests unitaires pour valider votre fonction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "321dbc03",
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.default_rng(0)\n",
    "x = rng.standard_normal(64) + 1j * rng.standard_normal(64)\n",
    "L = len(x)\n",
    "X_tfd = TFD(x, L)\n",
    "X_np = np.fft.fft(x, n=L)\n",
    "\n",
    "assert np.allclose(X_tfd, X_np), f\"Erreur pour L=N : \\\n",
    "                                    \\n Fonction NumPy (longueur {len(X_np)}) : {X_np}\\n \\\n",
    "                                    Votre fonction (longueur {len(X_tfd)}) : {X_tfd}\"\n",
    "\n",
    "L = 128\n",
    "X_tfd = TFD(x, L)\n",
    "X_np = np.fft.fft(x, n=L)\n",
    "\n",
    "assert np.allclose(X_tfd, X_np), f\"Erreur pour L>N : \\\n",
    "                                    \\n Fonction NumPy (longueur {len(X_np)}) : {X_np}\\n \\\n",
    "                                    Votre fonction (longueur {len(X_tfd)}) : {X_tfd}\"\n",
    "\n",
    "L = 32\n",
    "X_tfd = TFD(x, L)\n",
    "X_np = np.fft.fft(x, n=L)\n",
    "\n",
    "assert np.allclose(X_tfd, X_np), f\"Erreur pour L<N : \\\n",
    "                                    \\n Fonction NumPy (longueur {len(X_np)}) : {X_np}\\n \\\n",
    "                                    Votre fonction (longueur {len(X_tfd)}) : {X_tfd}\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f7f1d22",
   "metadata": {},
   "source": [
    "Avant de tester notre fonction, il nous faut aussi calculer l'axe fréquentiel (*np.fft.fftfreq*). Recodez la fonction fftfreq de NumPy, en vous aidant de la documentation : https://numpy.org/devdocs/reference/generated/numpy.fft.fftfreq.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4dc41fc6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "# Fonction de calcul de l'axe fréquentiel\n",
    "def TFD_freq(N, Te):\n",
    "    if N%2: # N impair\n",
    "        return np.concatenate([np.arange(0,(N-1)/2+1),np.arange(-(N-1)/2,0)]) / (N*Te)\n",
    "    else: # N pair\n",
    "        return np.concatenate([np.arange(0,N/2),np.arange(-N/2,0)]) / (N*Te)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c53f2319",
   "metadata": {},
   "source": [
    "2 tests unitaires pour valider votre fonction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4dca9eb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 50\n",
    "fe = 1000\n",
    "own_fftfreq = TFD_freq(N, 1/fe)\n",
    "np_fftfreq = np.fft.fftfreq(N, 1/fe)\n",
    "assert np.allclose(own_fftfreq, np_fftfreq), f\"Erreur pour N pair : \\\n",
    "                                            \\n Fonction NumPy (longueur {len(np_fftfreq)}) : {np_fftfreq}\\n \\\n",
    "                                            Votre fonction (longueur {len(own_fftfreq)}) : {own_fftfreq}\"\n",
    "\n",
    "N = 51\n",
    "fe = 2048\n",
    "own_fftfreq = TFD_freq(N, 1/fe)\n",
    "np_fftfreq = np.fft.fftfreq(N, 1/fe)\n",
    "assert np.allclose(own_fftfreq, np_fftfreq), f\"Erreur pour N impair : \\\n",
    "                                            \\n Fonction NumPy (longueur {len(np_fftfreq)}) : {np_fftfreq}\\n \\\n",
    "                                            Votre fonction (longueur {len(own_fftfreq)}) : {own_fftfreq}\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88e52855",
   "metadata": {},
   "source": [
    "Une dernière étape avant de tester sur un signal : il nous faut coder également *fftshift*, permettant de recentrer la transformée et l'axe fréquentiel pour que la fréquence 0 soit au centre. Développez la fonction en vous aidant de la documentation de la fonction : https://numpy.org/devdocs/reference/generated/numpy.fft.fftshift.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5e346ad2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "# Fonction de recentrage des fréquences\n",
    "def TFD_shift(x):\n",
    "    N = len(x)\n",
    "    if N%2: # N impair\n",
    "        return np.concatenate([x[(N+1)//2:],x[:(N+1)//2]])\n",
    "    else: # N pair\n",
    "        return np.concatenate([x[N//2:],x[:N//2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab6a350d",
   "metadata": {},
   "source": [
    "2 tests unitaires pour valider votre fonction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0b94c31d",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 50\n",
    "x = np.random.randint(0,100,size=(N))\n",
    "own_fftshift = TFD_shift(x)\n",
    "np_fftshift = np.fft.fftshift(x)\n",
    "assert (own_fftshift==np_fftshift).all(), f\"Erreur pour N pair : \\\n",
    "                                            \\n Fonction NumPy (longueur {len(np_fftshift)}) : {np_fftshift}\\n \\\n",
    "                                            Votre fonction (longueur {len(own_fftshift)}) : {own_fftshift}\"\n",
    "N = 51\n",
    "x = np.random.randint(0,100,size=(N))\n",
    "own_fftshift = TFD_shift(x)\n",
    "np_fftshift = np.fft.fftshift(x)\n",
    "assert (own_fftshift==np_fftshift).all(), f\"Erreur pour N impair : \\\n",
    "                                            \\n Fonction NumPy (longueur {len(np_fftshift)}) : {np_fftshift}\\n \\\n",
    "                                            Votre fonction (longueur {len(own_fftshift)}) : {own_fftshift}\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1bab856",
   "metadata": {},
   "source": [
    "On peut maintenant créer un signal, calculer sa TFD et afficher le spectre d'amplitude, comme lors du TP3 (exercice 2).\n",
    "\n",
    "Créez et affichez le signal suivant : \n",
    "\\begin{equation*}\n",
    "    s(t) = \\sin(2 \\pi f_{0} t)\n",
    "\\end{equation*}\n",
    "\n",
    "Avec $f_{0} = 50 Hz$. Le signal évoluera durant 0.1 seconde avec une fréquence d'échantillonage $f_e = 1000 Hz$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1be44cbd",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création et affichage de s(t)\n",
    "\n",
    "# Création de l'axe temporel\n",
    "T = 0.1 # Durée du signal\n",
    "fe = 1000 # Fréquence d'échantillonage\n",
    "t = np.arange(0,T,1/fe)\n",
    "\n",
    "# Création du signal sinuisoïdal\n",
    "f0 = 50 # Fréquence de la sinusoïde\n",
    "s = np.sin(2*np.pi*f0*t)\n",
    "\n",
    "# Afficage du signal\n",
    "plt.figure()\n",
    "plt.plot(t,s,label=\"s(t)\")\n",
    "plt.xlabel(\"Temps (s)\")\n",
    "plt.ylabel(\"Intensité\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4998277",
   "metadata": {},
   "source": [
    "Calculez maintenant avec vos superbes fonctions la transformée de Fourier directe de $s(t)$, et affichez le spectre d'amplitude."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6df9acd7",
   "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",
    "# Calcul de la TFD de s(t) et affichage du spectre d'amplitude\n",
    "S = TFD_shift(TFD(s,len(s)))\n",
    "freq_S = TFD_shift(TFD_freq(len(s),1/fe))\n",
    "\n",
    "amplitude_S = np.abs(S) / len(S) # Récupération du module de S\n",
    "\n",
    "# Affichage du spectre d'amplitude\n",
    "plt.figure()\n",
    "plt.stem(freq_S, amplitude_S, markerfmt=\" \")\n",
    "plt.title(\"Amplitude de S(f)\")\n",
    "plt.xlabel(\"Fréquences (Hz)\")\n",
    "plt.ylabel(\"Amplitude\")\n",
    "plt.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54613115",
   "metadata": {},
   "source": [
    "Vous aimez coder ? *(\"OUI!\" répondent-ils tous en choeur)*, et bien on va coder les fonctions inverses maintenant !\n",
    "\n",
    "Commençons par la transformée de Fourier discrète inverse (ITFD). La formule est la suivante :\n",
    "\n",
    "\\begin{equation*}\n",
    "    x[n]= \\frac{1}{L} \\sum_{k=0}^{L-1} X[k] e^{j2π \\frac{k}{L} n}\n",
    "\\end{equation*}\n",
    "\n",
    "On a toujours nos 4 variables $N,n,L$ et $K$, mais cette fois-ci, c'est bien $N$, la longueur du signal temporel en sortie, qui doit être indiqué en paramètre d'entrée de la fonction. De la même manière que précédemment, on peut avoir $N \\neq L$, avec toujours 3 cas de figures:\n",
    "\n",
    "- $N=L$ : le plus simple, aucune modification n'est à apporter sur le signal d'entrée\n",
    "- $N<L$ : on coupe le signal d'entrée en ne gardant que les $N$ premières valeurs\n",
    "- $N>L$ : on agrandit le signal d'entrée en rajoutant des zéros à la fin, afin qu'il soit de taille $N$.\n",
    "\n",
    "A votre clavier ! Prêts ? Codez !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9fbc261a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "# Fonction de transformée de Fourier inverse directe\n",
    "\n",
    "def ITFD(X,N):\n",
    "    X_pad = padding(X,N)\n",
    "    x = np.zeros((N),dtype=complex)\n",
    "    for n in range(N):\n",
    "        sum_X = 0\n",
    "        for k in range(N):\n",
    "            sum_X += X[k] * np.exp(2*np.pi*k*n/N*1j)\n",
    "        x[n] = sum_X / N\n",
    "    return x\n",
    "\n",
    "# Une version un peu plus optimisée\n",
    "def ITFD(X,N):\n",
    "    X_pad = padding(X,N)\n",
    "    k = np.arange(N) # On calcule un vecteur range de N, histoire d'éviter une boucle supplémentaire et donc d'accélerer le calcul\n",
    "    x = np.zeros((N), dtype=complex)\n",
    "    for n in range(N):\n",
    "        x[n] = (X_pad*np.exp(2*np.pi*k*n/N*1j)).sum() / N\n",
    "    return x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3f11f0f",
   "metadata": {},
   "source": [
    "3 tests unitaires pour valider votre fonction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9b5b0be2",
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.default_rng(0)\n",
    "X = rng.standard_normal(64) + 1j * rng.standard_normal(64)\n",
    "L = len(X)\n",
    "\n",
    "x_itfd = ITFD(X, L)\n",
    "x_np = np.fft.ifft(X, n=L)\n",
    "\n",
    "assert np.allclose(x_itfd, x_np), f\"Erreur pour N=L : \\\n",
    "                                    \\n Fonction NumPy (longueur {len(x_np)}) : {x_np}\\n \\\n",
    "                                    Votre fonction (longueur {len(x_itfd)}) : {x_itfd}\"\n",
    "\n",
    "L = 128\n",
    "x_itfd = ITFD(X, L)\n",
    "x_np = np.fft.ifft(X, n=L)\n",
    "\n",
    "assert np.allclose(x_itfd, x_np), f\"Erreur pour N<L (zero-pad) : \\\n",
    "                                    \\n Fonction NumPy (longueur {len(x_np)}) : {x_np}\\n \\\n",
    "                                    Votre fonction (longueur {len(x_itfd)}) : {x_itfd}\"\n",
    "\n",
    "X_long = rng.standard_normal(96) + 1j * rng.standard_normal(96)  # N = 96\n",
    "L = 32\n",
    "\n",
    "x_itfd = ITFD(X_long, L)\n",
    "x_np = np.fft.ifft(X_long, n=L)\n",
    "\n",
    "assert np.allclose(x_itfd, x_np), f\"Erreur pour N>L (troncature) : \\\n",
    "                                    \\n Fonction NumPy (longueur {len(x_np)}) : {x_np}\\n \\\n",
    "                                    Votre fonction (longueur {len(x_itfd)}) : {x_itfd}\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "932c9d2e",
   "metadata": {},
   "source": [
    "Et pour finir cette longue session de code, une dernière fonction à implémenter : l'inverse de *fftshift* (*iffshift*). Comme précédemment, je vous invite à aller voir la documentation pour vous aider dans le développement: https://numpy.org/doc/2.1/reference/generated/numpy.fft.ifftshift.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "deb3db5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A COMPLETER\n",
    "# Fonction inverse de recentrage des fréquences\n",
    "def ITFD_shift(x):\n",
    "    N = len(x)\n",
    "    return np.concatenate([x[N//2:],x[:N//2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26b5f718",
   "metadata": {},
   "source": [
    "2 tests unitaires pour valider votre fonction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9d38aa9c",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 50\n",
    "x = np.random.randint(0, 100, size=(N))\n",
    "own_ifftshift = ITFD_shift(x)\n",
    "np_ifftshift = np.fft.ifftshift(x)\n",
    "\n",
    "assert (own_ifftshift == np_ifftshift).all(), f\"Erreur pour N pair : \\\n",
    "                                            \\n Fonction NumPy (longueur {len(np_ifftshift)}) : {np_ifftshift}\\n \\\n",
    "                                            Votre fonction (longueur {len(own_ifftshift)}) : {own_ifftshift}\"\n",
    "\n",
    "N = 51\n",
    "x = np.random.randint(0, 100, size=(N))\n",
    "own_ifftshift = ITFD_shift(x)\n",
    "np_ifftshift = np.fft.ifftshift(x)\n",
    "\n",
    "assert (own_ifftshift == np_ifftshift).all(), f\"Erreur pour N impair : \\\n",
    "                                            \\n Fonction NumPy (longueur {len(np_ifftshift)}) : {np_ifftshift}\\n \\\n",
    "                                            Votre fonction (longueur {len(own_ifftshift)}) : {own_ifftshift}\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8116421c",
   "metadata": {},
   "source": [
    "Calculez maintenant vos fonction inverses pour recrée $s(t)$ à partir de $S(f)$, et affichez sur le même graphique la courbe d'origine et celle en sortie de transformée inverse."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "633ea53b",
   "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",
    "# Transformée inverse de S(f) et affichage\n",
    "s_prime = ITFD(ITFD_shift(S),len(S))\n",
    "\n",
    "# La sortie étant complexe, il ne faut prendre que la partie réelle du signal (la partie imaginaire est en réalité quasi nulle)\n",
    "real_s_prime = np.real(s_prime)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(t, s, label=\"Original\")\n",
    "plt.plot(t, real_s_prime, label=\"Après ITFD\")\n",
    "plt.title(\"Signal s(t)\")\n",
    "plt.xlabel(\"Temps (s)\")\n",
    "plt.ylabel(\"Amplitude\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14c898b8",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Exercice 2 : La science réside dans les détails\n",
    "\n",
    "Si vous avez fini l'exercice 1, félicitations ! Pour la suite du TP, vous pouvez soit reprendre vos fonctions de l'exercice 1, soit utiliser celles de NumPy. \n",
    "\n",
    "Vous avez pu voir précédemment qu'on peut définir une taille différente pour le spectre fréquentiel ($L$ dans $fft$) et pour le signal temporel ($N$ pour *ifft*). On va donc maintenant regarder en détail l'utilité de ces paramètres."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8dae6c3",
   "metadata": {},
   "source": [
    "Créez le signal $x(t)$, toujours une sinusoïde mais de fréquence $12,5$ Hz. Le signal évoluera durant 1 secondes à une fréquence d'échantillonnage $f_e$ = 500 Hz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3b2875ee",
   "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 de x(t)\n",
    "\n",
    "# Création de l'axe temporel\n",
    "T_x = 1 # Durée du signal\n",
    "fe = 500 # Fréquence d'échantillonage\n",
    "t_x = np.arange(0,T_x,1/fe)\n",
    "\n",
    "# Création du signal sinuisoïdal\n",
    "f0 = 12.5 # Fréquence de la sinusoïde\n",
    "x = np.sin(2*np.pi*f0*t_x)\n",
    "\n",
    "# Afficage du signal\n",
    "plt.figure()\n",
    "plt.plot(t_x,x,label=\"x(t)\")\n",
    "plt.xlabel(\"Temps (s)\")\n",
    "plt.ylabel(\"Intensité\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c46726d",
   "metadata": {},
   "source": [
    "Calculez maintenant la transformée de Fourier du signal et affichez le spectre d'amplitude."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "91dce36a",
   "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",
    "# Calcul de la TFD de x(t) et affichage du spectre d'amplitude\n",
    "X = TFD_shift(TFD(x,len(x)))\n",
    "freq_X = TFD_shift(TFD_freq(len(x),1/fe))\n",
    "\n",
    "amplitude_X = np.abs(X) / len(X) # Récupération du module de X\n",
    "\n",
    "# Affichage du spectre d'amplitude\n",
    "plt.figure()\n",
    "plt.stem(freq_X, amplitude_X, markerfmt=\" \")\n",
    "plt.title(\"Amplitude de X(f)\")\n",
    "plt.xlabel(\"Fréquences (Hz)\")\n",
    "plt.ylabel(\"Amplitude\")\n",
    "plt.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb72ba77",
   "metadata": {},
   "source": [
    "**_QUESTION :_** Est-ce que le spectre vous paraît correct ? Que constatez-vous ?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc12cf8a",
   "metadata": {},
   "source": [
    "**_REPONSE :_** Normalement, on devrait avoir 2 pics d'amplitude 0.5 à -12,5 et -12,5 Hz. Cependant, on voit ici deux pics aux alentours de 0.35, mais tout autour de ces pics des fréquences qui normalement n'existent pas dans le signal d'origine."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb862983",
   "metadata": {},
   "source": [
    "Construisez maintenant le signal $y(t)$, qui exactement le signal $x(t)$ mais évoluant durant 1,04 secondes, affichez le signal et son spectre d'amplitude après TFD."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a3b1738c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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 de y(t), et affichage du spectre d'amplitude de Y(f)\n",
    "\n",
    "# Création de l'axe temporel\n",
    "T_y = 1.04 # Durée du signal\n",
    "fe = 500 # Fréquence d'échantillonage\n",
    "t_y = np.arange(0,T_y,1/fe)\n",
    "\n",
    "# Création du signal sinuisoïdal\n",
    "f0 = 12.5 # Fréquence de la sinusoïde\n",
    "y = np.sin(2*np.pi*f0*t_y)\n",
    "\n",
    "# Afficage du signal\n",
    "plt.figure()\n",
    "plt.plot(t_y,y,label=\"y(t)\")\n",
    "plt.xlabel(\"Temps (s)\")\n",
    "plt.ylabel(\"Intensité\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "# Calcul de la TFD de y(t)\n",
    "Y = TFD_shift(TFD(y,len(y)))\n",
    "freq_Y = TFD_shift(TFD_freq(len(y),1/fe))\n",
    "\n",
    "amplitude_Y = np.abs(Y) / len(Y) # Récupération du module de X\n",
    "\n",
    "# Affichage du spectre d'amplitude\n",
    "plt.figure()\n",
    "plt.stem(freq_Y, amplitude_Y, markerfmt=\" \")\n",
    "plt.title(\"Amplitude de Y(f)\")\n",
    "plt.xlabel(\"Fréquences (Hz)\")\n",
    "plt.ylabel(\"Amplitude\")\n",
    "plt.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7cfbb466",
   "metadata": {},
   "source": [
    "**_QUESTION :_** Que constatez-vous concernant le spectre d'amplitude de $Y(f)$ par rapport à celui de $X(f)$ ?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3935c57",
   "metadata": {},
   "source": [
    "**_REPONSE :_** On remarque que le spectre d'amplitude de $Y(f)$ correspond à celui attendu avec uniquement deux pics à -12,5 et 12,5 Hz, d'amplitude 0.5."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e52cfc6e",
   "metadata": {},
   "source": [
    "Vous devriez donc avoir deux spectres différents alors que vous avez le même signal en entrée, à la seul différence que $y(t)$ évolue durant 1.04 secondes contre 1 secondes pour $x(t)$. On a ici un **problème de fuite spectale**. Le pas de votre axe fréquentiel que vous avez défini dépend de la durée de votre signal : \n",
    "\n",
    "\\begin{equation*}\n",
    "    \\Delta f = \\frac{1}{T} = \\frac{f_e}{L}\n",
    "\\end{equation*}\n",
    "\n",
    "Avec $T$ la durée du signal, et $L$ la taille du tableau représentant votre signal en fréquentiel.\n",
    "\n",
    "Dans le premier cas, votre pas fréquentiel est donc égal à 1 Hz, ce qui signifie que les fréquences détectées sont espacées de 1 Hz (0, 1, 2, 3, etc...). 12,5 Hz n'étant pas entier, il est normal qu'il ne soit pas détecté. Dans le deuxième cas, le pas fréquentiel tombe à environ 0.96 Hz. La fréquence de 12.5 Hz tombe pile sur l'un des bins de l'axe fréquentiel.\n",
    "\n",
    "Plus généralement, dans le cas d'un signal périodique (comme ici), on évite une fuite spectrale lorsque le signal évolue durant un nombre entier $P$ de périodes complètes. Dans le premier cas, on peut voir que le signal évolue sur 12 périodes complètes, et une 13ème incomplète. En revanche, le signal $y(t)$ évolue lui durant 13 périodes complètes.\n",
    "\n",
    "Ici, notre signal peut être définit sur autant de temps qu'on le veut puisqu'il est stable. Cependant, pour la majorité des signaux à analyser, on ne peut leurs évolutions. De ce fait, on peut alors **allonger** le signal avec un zero-padding, ce que fait la fonction *fft*.\n",
    "\n",
    "Recalculez *X(f)* en précisant la taille de sortie de l'axe fréquentiel. Pour cela, calculez le nombre de points nécessaires pour garantir un nombre entier de périodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "59f695e6",
   "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",
    "# Transformée de Fourier de x(t) en précisant la taille du spectre fréquentiel afin de garantir un nombre entier de périodes\n",
    "\n",
    "# Dans un premier temps, on calcule le nombre de périodes effectuées durant le temps T\n",
    "nb_periodes_x = T_x*f0\n",
    "# On vérifie si nb_periodes_x  est entier, et sinon, on prend la valeur entière supérieure\n",
    "if (nb_periodes_x.is_integer()):\n",
    "    L_prime = len(x)\n",
    "else:\n",
    "    T_prime = np.ceil(nb_periodes_x)/f0 # On calcule le nouveau temps garantissant un nombre entier de périodes\n",
    "    L_prime = int(T_prime*fe)\n",
    "\n",
    "X_pad = TFD_shift(TFD(x,L_prime))\n",
    "freq_X_pad = TFD_shift(TFD_freq(L_prime,1/fe))\n",
    "\n",
    "amplitude_X_pad = np.abs(X_pad) / len(X_pad) # Récupération du module de X_pad\n",
    "\n",
    "# Affichage du spectre d'amplitude\n",
    "plt.figure()\n",
    "plt.stem(freq_X_pad, amplitude_X_pad, markerfmt=\" \")\n",
    "plt.title(f\"Amplitude de X(f) étendu à {T_prime} secondes\")\n",
    "plt.xlabel(\"Fréquences (Hz)\")\n",
    "plt.ylabel(\"Amplitude\")\n",
    "plt.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64adc0bb",
   "metadata": {},
   "source": [
    "**_QUESTION :_** Est-ce que la transformée de Fourier obtenue est meilleure ?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ff16c4e",
   "metadata": {},
   "source": [
    "**_REPONSE :_** Elle est meilleure, même si elle n'est pas parfaite. Les 2 pics à 12.5 et -12.5 Hz ont une amplitude proche de 0.5, et les fréquences aux alentours ont une amplitude beaucoup plus faible."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5af50826",
   "metadata": {},
   "source": [
    "**_QUESTION :_** Pourquoi la TF obtenue n'est pas totalement parfaite ?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c259a137",
   "metadata": {},
   "source": [
    "**_REPONSE :_** On a certes allongé le signal, mais en faisant un zéro padding. De ce fait, le signal n'est plus tout à fait périodique."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8daf8d48",
   "metadata": {},
   "source": [
    "En effet, agrandir le vecteur temporel avec un zero-padding ne corrige pas une fuite spectrale. \n",
    "\n",
    "Concrètement, l'utilité du zero-padding avant une FFT sert avant tout à augmenter le nombre de points en fréquentiels, et ainsi améliorer la résolution fréquentielle $\\Delta f$. Cela permet de mieux analyser les composantes du signal. De plus, sans rentrer dans les détails de calcul, la FFT est d'autant plus efficace à calculer lorsque $N = 2^{k}$ avec $k \\in \\N$. \n",
    "\n",
    "Pour corriger une fuite spectrale, il est préférable de fenêtrer le signal par multiplication avec une fenêtre de Hann, ou une fenêtre de Hamming par exemple. ces fenêtres servent à adoucir les bords d’un signal fini avant une FFT, afin de réduire les discontinuités périodiques. \n",
    "\n",
    "On va appliquer une fenêtre de Hann dans un premier temps sur $x(t)$ via la fonction *np.hanning*. Calculer $h(t)$, la fenêtre de Hann, et $w(t) = x(t) \\times h(t)$. Affichez ensuite les courbes $x(t)$, $h(t)$ et $w(t)$ dans 3 graphes différents."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "d5e0ed78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Création de w(t), le fenêtrage de x(t) par h(t), une fenêtre de Hann, et affichage des 3 courbes\n",
    "h = np.hanning(len(x))\n",
    "w = x*h\n",
    "\n",
    "# Affichage du spectre d'amplitude\n",
    "plt.subplots(3,1)\n",
    "plt.subplot(311)\n",
    "plt.plot(t_x,x)\n",
    "plt.title(\"x(t)\")\n",
    "plt.subplot(312)\n",
    "plt.plot(t_x,h)\n",
    "plt.title(\"h(t)\")\n",
    "plt.subplot(313)\n",
    "plt.plot(t_x,w)\n",
    "plt.title(\"w(t)\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b0cc160",
   "metadata": {},
   "source": [
    "Si vous avez bien réalisez le fenêtrage, vous pouvez constater que $w(t)$ a une fréquence similaire que $x(t)$, avec les bords adoucis. Cependant, l'énergie globale du signal est inévitablement plus faible que l'original.\n",
    "\n",
    "On va maintenant calculer la transformée de Fourier de $w(t)$. Pour compenser la perte d'énergie causée par le fenêtrage, il faut ensuite diviser $W(f)$ par le gain moyen de $h(t)$ (à savoir la moyenne de $h(t)$).\n",
    "\n",
    "Affichez le spectre d'amplitude de $W(f)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "63b6ae6e",
   "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",
    "# Calcul de la TFD de w(t) et affichage du spectre d'amplitude\n",
    "W = TFD_shift(TFD(w,len(w)))\n",
    "W = W / np.mean(h)\n",
    "\n",
    "freq_W = TFD_shift(TFD_freq(len(w),1/fe))\n",
    "\n",
    "amplitude_W = np.abs(W) / len(W) # Récupération du module de W\n",
    "\n",
    "# Affichage du spectre d'amplitude\n",
    "plt.figure()\n",
    "plt.stem(freq_W, amplitude_W, markerfmt=\" \")\n",
    "plt.title(\"Amplitude de W(f)\")\n",
    "plt.xlabel(\"Fréquences (Hz)\")\n",
    "plt.ylabel(\"Amplitude\")\n",
    "plt.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4d919bf",
   "metadata": {},
   "source": [
    "**_QUESTION :_** Est-ce que le fenêtrage de Hann améliore le spectre d'amplitude ?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf9a4463",
   "metadata": {},
   "source": [
    "**_REPONSE :_** Oui, on se rapproche plus de ce qui est attendu. Les deux pics ont une amplitude proche 0.5, mais sont plus larges, supposants que plusieurs fréquences très proches ont une forte amplitude. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d25cf7e",
   "metadata": {},
   "source": [
    "Réalisez les opérations précédentes, mais en appliquant un fenêtrage de Hamming (*np.hamming*), et un fenêtrage de Blackman (*np.blackman*)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "01b0c378",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Mêmes opérations que précédemment mais avec une fenêtre de Hamming\n",
    "h = np.hamming(len(x))\n",
    "w = x*h\n",
    "\n",
    "# Affichage du spectre d'amplitude\n",
    "plt.subplots(3,1)\n",
    "plt.subplot(311)\n",
    "plt.plot(t_x,x)\n",
    "plt.title(\"x(t)\")\n",
    "plt.subplot(312)\n",
    "plt.plot(t_x,h)\n",
    "plt.title(\"h(t)\")\n",
    "plt.subplot(313)\n",
    "plt.plot(t_x,w)\n",
    "plt.title(\"w(t)\")\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Calcul de la TFD de w(t) et affichage du spectre d'amplitude\n",
    "W = TFD_shift(TFD(w,len(w)))\n",
    "W = W / np.mean(h)\n",
    "\n",
    "freq_W = TFD_shift(TFD_freq(len(w),1/fe))\n",
    "\n",
    "amplitude_W = np.abs(W) / len(W) # Récupération du module de W\n",
    "\n",
    "# Affichage du spectre d'amplitude\n",
    "plt.figure()\n",
    "plt.stem(freq_W, amplitude_W, markerfmt=\" \")\n",
    "plt.title(\"Amplitude de W(f)\")\n",
    "plt.xlabel(\"Fréquences (Hz)\")\n",
    "plt.ylabel(\"Amplitude\")\n",
    "plt.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "f0d5181c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A COMPLETER\n",
    "# Mêmes opérations que précédemment mais avec une fenêtre de Blackman\n",
    "h = np.blackman(len(x))\n",
    "w = x*h\n",
    "\n",
    "# Affichage du spectre d'amplitude\n",
    "plt.subplots(3,1)\n",
    "plt.subplot(311)\n",
    "plt.plot(t_x,x)\n",
    "plt.title(\"x(t)\")\n",
    "plt.subplot(312)\n",
    "plt.plot(t_x,h)\n",
    "plt.title(\"h(t)\")\n",
    "plt.subplot(313)\n",
    "plt.plot(t_x,w)\n",
    "plt.title(\"w(t)\")\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Calcul de la TFD de w(t) et affichage du spectre d'amplitude\n",
    "W = TFD_shift(TFD(w,len(w)))\n",
    "W = W / np.mean(h)\n",
    "\n",
    "freq_W = TFD_shift(TFD_freq(len(w),1/fe))\n",
    "\n",
    "amplitude_W = np.abs(W) / len(W) # Récupération du module de W\n",
    "\n",
    "# Affichage du spectre d'amplitude\n",
    "plt.figure()\n",
    "plt.stem(freq_W, amplitude_W, markerfmt=\" \")\n",
    "plt.title(\"Amplitude de W(f)\")\n",
    "plt.xlabel(\"Fréquences (Hz)\")\n",
    "plt.ylabel(\"Amplitude\")\n",
    "plt.plot()\n",
    "plt.show()"
   ]
  }
 ],
 "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
}
