{ "cells": [ { "cell_type": "markdown", "id": "9113be64-b859-4517-8bae-59c82152acea", "metadata": {}, "source": [ "Notebook Jupyter UTC MT12 \n", "$$ \\text{TP} 4 \\;: \\; \\textbf{Transformée de Fourier Discrète}$$\n", "###### Cette cellule est une cellule Markdown" ] }, { "cell_type": "markdown", "id": "fea8551e-9785-46c3-b26e-5061c2e8c1b5", "metadata": {}, "source": [ "### L'objectif principal de ce TP est de manipuler la transformée de Fourier discrète." ] }, { "cell_type": "markdown", "id": "607f0445-f856-4429-96a1-53c61669cbb8", "metadata": {}, "source": [ "#### Plan \n", "[1. Implémentation de la matrice de transformée de Fourier discrète (TFD ou DFT)](#1.-Implémentation-de-la-matrice-de-transformée-de-Fourier-discrète-(-TFD-ou-DFT-))\n", "\n", "[2. FFT et \"débruitage\" d'un signal](#2.-FFT-et-débruitage-d-'-un-signal)\n", " " ] }, { "cell_type": "markdown", "id": "8ddd4c27-6d9e-4bad-881c-a1f8c33cfc57", "metadata": {}, "source": [ "# 1. Implémentation de la matrice de transformée de Fourier discrète (TFD ou DFT)" ] }, { "cell_type": "markdown", "id": "9a4149e1-185e-46c2-b651-409a27f76cfd", "metadata": {}, "source": [ "## 1.1. Rappels sur la transformée de Fourier discrète" ] }, { "cell_type": "markdown", "id": "ebdc6469-3f5e-4e4d-b91d-3b8c5badbc48", "metadata": {}, "source": [ "On rappelle que la transformée de Fourier discrète (~TFD ou DFT) d'ordre $N$ ($N\\geq 2$) est l'application linéaire $\\mathcal{F}_N$ définie de $\\mathbb{C}^N$ dans $\\mathbb{C}^N$, qui à un vecteur $\\textbf{y}=(y_0,...,y_{N-1})^\\top \\in \\mathbb{C}^N$ associe le vecteur $\\textbf{Y}=(Y_0,...,Y_{N-1})^\\top = \\mathcal{F}_N \\textbf{y} \\in \\mathbb{C}^N$,\n", "défini par $$Y_n = \\frac{1}{N} \\sum_{k=0}^{N-1} y_k\\, \\omega_N^{-nk},\\qquad n=0,...,N-1,$$ où $\\omega_N$ désigne le nombre complexe suivant $\\omega_N = \\text{e}^{2i\\frac\\pi N}.$" ] }, { "cell_type": "markdown", "id": "76b84378-0e88-4051-863e-7360665cc1b0", "metadata": {}, "source": [ "## 1.2 Questions" ] }, { "cell_type": "markdown", "id": "f2c4869f-20b0-4b6a-9779-9b44ab29c66e", "metadata": {}, "source": [ "### Q1.a. Justifier à la main l'écriture matricielle suivante de la TFD \\begin{align*} \\textbf{Y} = S_N \\, \\textbf{y},\\quad \\text{où} \\;\\; & \\quad S_N = \\frac{1}{N}\\,\\, \\overline{\\Omega}_N,\\\\ \\text{avec} & \\quad \\Omega_N : \\text{matrice carrée de dim$=N$ de terme général} \\\\ & \\quad (\\Omega_N)_{nk} = \\text{e}^{2i\\pi \\frac{nk}{N}} = \\omega_N^{nk}, \\;0 \\leq n,k\\leq N-1.&\\end{align*}" ] }, { "cell_type": "markdown", "id": "8a1b7054-a710-4244-b88a-4f880ff5c3d6", "metadata": {}, "source": [ "Le produit matriciel $S_N \\, \\textbf{y}$ fournit un vecteur de dimension $N$ dont la n-ième composante est définie par:\n", "$$\n", "(S_N\\mathbf{y})_n = \\frac{1}{N} \\sum_{k=0}^{N-1} \\text{e}^{-2i\\pi \\frac{nk}{N}}y_k= \\frac{1}{N} \\sum_{k=0}^{N-1} \\omega_N^{-nk} y_k =Y_n \n", "$$" ] }, { "cell_type": "markdown", "id": "439bc71d-860e-4509-99df-e85c021f3278", "metadata": {}, "source": [ "### Q1.b. Justifier à la main que l'inverse de la matrice $S_N$ vérifie $$ (S_N)^{-1} = \\Omega_N.$$ Autrement dit, la transformée de Fourier discrète inverse (TFDI) a pour représentation matricielle la matrice $\\Omega_N$." ] }, { "cell_type": "markdown", "id": "a2e665fb-777e-4da9-994d-9465bed86066", "metadata": {}, "source": [ "Le prodtui matriciel $\\Omega_N S_N$ fournit une matrice carrée de dimension $N$ dont l'entrée à la ligne $n$ colonne $k$ est définie par:\n", "\\begin{eqnarray*}\n", "(\\Omega_N S_N)_{nk} &= \\frac{1}{N} \\sum_{l=0}^{N-1} (\\Omega_N)_{nl} (S_N)_{lk} \\\\\n", "& = \\frac{1}{N} \\sum_{l=0}^{N-1} \\omega_N^{nl} \\omega_N^{-lk}\\\\\n", "& = \\frac{1}{N} \\sum_{l=0}^{N-1} \\omega_N^{l(n-k)} \n", "\\end{eqnarray*}\n", "\n", "* Quand $n=k$, $\\frac{1}{N} \\sum_{l=0}^{N-1} \\omega_N^{l(n-k)}= \\frac{1}{N} \\sum_{l=0}^{N-1} 1=1$\n", "* Quand $n\\neq k$, $\\frac{1}{N} \\sum_{l=0}^{N-1} \\omega_N^{l(n-k)}= \\frac{1}{N} \\frac{1- \\omega_N^{N(n-k)}}{1-\\omega_N^{(n-k)}}=0$" ] }, { "cell_type": "markdown", "id": "c229ca88-c5c2-4105-a83f-36d4c4bb0500", "metadata": {}, "source": [ "### Q2 Implémentation naïve de la TFD" ] }, { "cell_type": "markdown", "id": "db02c84a-4493-47a3-ae97-0828942e9180", "metadata": {}, "source": [ "#### Q2.a. Pour un entier strictement positif $N$, définir une fonction $\\textbf{TFD1}$ qui implémente la matrice $S_N$ en utilisant deux boucles for." ] }, { "cell_type": "code", "execution_count": 1, "id": "65407227-fe84-4f29-a235-e495d0e05f48", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import cmath as cm #importe les complexes\n", "import scipy as sc" ] }, { "cell_type": "markdown", "id": "f8f5bb4f-e1b6-44a5-a361-5ed1a422ad18", "metadata": {}, "source": [ "La fonction z.conjugate() calcule le conjugué du nombre complexe z, cette fonction s’applique aussi aux matrices." ] }, { "cell_type": "code", "execution_count": 2, "id": "e92d1068-8a40-4338-bfa0-e1a1b3b010bc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A= [[0.+0.j 0.+0.j]\n", " [3.+2.j 0.+0.j]]\n", "conjA= [[0.-0.j 0.-0.j]\n", " [3.-2.j 0.-0.j]]\n" ] } ], "source": [ "complex(0,1) #retourne i (s'appelle 'j' ici)\n", "cm.exp(complex(0,1)*np.pi/2) # retourne exp(-i pi/2)\n", "A=np.zeros([2,2],dtype=np.complex128) # retourne une matrice 2*2 de complexes de parties réelle et imaginaire nulle\n", "A[1,0]= 3+2*complex(0,1) #place le complexe 3+2i à l'intersection ligne 2 et colonne 1\n", "T=A.conjugate() # retourne la matrice conjuguée de A \n", "print('A=',A)\n", "print('conjA=',T)\n", "# \"A@B\" et \"A.dot(B)\" désignent la produit matriciel de A et B." ] }, { "cell_type": "code", "execution_count": 4, "id": "6276e391-72c3-408d-8049-caa1dc76d997", "metadata": {}, "outputs": [], "source": [ "def TFD1 (N):\n", " omegaN=cm.exp(2*complex(0,1)*np.pi/N)\n", " OMEGAN=np.zeros([N,N],dtype=np.complex128)\n", " for i in range(N):\n", " for k in range(N):\n", " # OMEGAN[i][k]= omegaN**(i*k); alternative\n", " OMEGAN[i,k]= omegaN**(i*k)\n", " return OMEGAN.conjugate()/N" ] }, { "cell_type": "code", "execution_count": 6, "id": "0ce41205-8505-4cc8-9030-4352a5cf9b2e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.33333333-0.j 0.33333333-0.j 0.33333333-0.j ]\n", " [ 0.33333333-0.j -0.16666667-0.28867513j -0.16666667+0.28867513j]\n", " [ 0.33333333-0.j -0.16666667+0.28867513j -0.16666667-0.28867513j]]\n" ] } ], "source": [ "print(TFD1(3))" ] }, { "cell_type": "markdown", "id": "1ab0cf09-3895-4897-a9e2-6a91d157734f", "metadata": {}, "source": [ "#### Q2.b Indiquer pourquoi le code de la fonction $\\textbf{TFD1}$ n'est pas très performant. " ] }, { "cell_type": "markdown", "id": "656f7639-3939-4fe2-9add-4fb61b9427c9", "metadata": {}, "source": [ "Double boucle \"for\"" ] }, { "cell_type": "markdown", "id": "e6e9d768-b664-4c31-b354-8f179fd2fac7", "metadata": {}, "source": [ "### Q3 Implémentation plus performante de la TFD que la méthode naïve. " ] }, { "cell_type": "markdown", "id": "ca22a9f9-bf0a-411b-abc9-875706792da6", "metadata": {}, "source": [ "##### Pour cette question, on considère le vecteur $\\bf{w}\\in\\mathbb{R}^N$ dont le $n$-ième composante est définie par $$w_n= \\sqrt{\\frac{2\\pi}{N}}\\, n\\, e^{i\\pi/4},\\quad n=0,...,N-1$$ " ] }, { "cell_type": "markdown", "id": "2d486977-381c-4e77-b5d1-39f085e601fc", "metadata": {}, "source": [ "#### Q3.a. Calculer à la main le produit $$\\bf{w} \\bf{w}^T = \\begin{pmatrix} 0\\\\ \\vdots\\\\ \\sqrt{\\frac{2\\pi}{N}}\\, (N-1)\\, e^{i\\pi/4} \\end{pmatrix} \\begin{pmatrix} 0 & \\ldots & \\sqrt{\\frac{2\\pi}{N}}\\, (N-1)\\, e^{i\\pi/4} \\end{pmatrix} \\; $$ \n", "On pourra simplement calculer les éléments $(\\bf{w} \\bf{w}^T)_{nk}$ de cette matrice." ] }, { "cell_type": "markdown", "id": "3aad5c64-0fdc-4567-8671-ec2e94557da6", "metadata": {}, "source": [ "Le produit $\\bf{w} \\bf{w}^T$ fournit une matrice carrée de taille $N$ dont l'entrée à la ligne $n$ colonne $k$ est définie par:\n", "\\begin{eqnarray*}\n", "(\\bf{w} \\bf{w}^T)_{nk} &= \\frac{2\\pi}{N}\\, n k\\, e^{i\\pi/2}= 2i\\pi \\frac{nk}{N}\n", "\\end{eqnarray*}" ] }, { "cell_type": "markdown", "id": "e922717e-7b07-44aa-a23a-a1318d29b38d", "metadata": {}, "source": [ "#### Q3.b. En déduire sur une feuille que $\\exp(\\bf{w}\\bf{w}^T)=\\Omega_N $ " ] }, { "cell_type": "markdown", "id": "9980a6a2-66ed-4131-aba0-414c248723f5", "metadata": {}, "source": [ "On en déduit que\n", "$$\\exp(\\bf{w}\\bf{w}^T)= \\left( (\\exp(2i\\pi \\frac{nk}{N})_{n,k}\\right)= \\left( (\\omega_{nk})_{n,k}\\right)= \\Omega_N$$" ] }, { "cell_type": "markdown", "id": "a5982b4f-5da5-4dbc-afe8-c351ac4bec76", "metadata": {}, "source": [ "#### Q3.c. Définir une fonction $\\textbf{TFD2}$ qui prend en entrée $N\\geq 1$, qui utilise $\\Omega_N = \\exp(\\bf{w} \\bf{w}^T)$ et qui renvoie la matrice $S_N$." ] }, { "cell_type": "code", "execution_count": 8, "id": "02f43903-a5f3-45ff-81be-55aeec01bb78", "metadata": {}, "outputs": [], "source": [ "def TFD2 (N):\n", " w=np.sqrt((2*np.pi)/N)*cm.exp(complex(0,1)*np.pi/4)\n", " n=np.arange(N)\n", " wn=w*n\n", " z=wn.reshape(N,1)\n", " Omega=np.exp(z.dot(z.T))\n", " return Omega.conjugate()/N" ] }, { "cell_type": "code", "execution_count": 9, "id": "ba60d1d7-2acd-421f-9989-413cecb42c2c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.33333333-0.j 0.33333333-0.j 0.33333333-0.j ]\n", " [ 0.33333333-0.j -0.16666667-0.28867513j -0.16666667+0.28867513j]\n", " [ 0.33333333-0.j -0.16666667+0.28867513j -0.16666667-0.28867513j]]\n" ] } ], "source": [ "TFD2(3)" ] }, { "cell_type": "markdown", "id": "7bf6a9c8-00a7-4826-8108-c9655a50c5ea", "metadata": {}, "source": [ "##### Q3.d. Comparer les temps d'exécution des fonctions $\\textbf{TFD1}$ et $\\textbf{TFD2}$ pour $N=100$, $200$, $300$ et $400$. Pour ce faire on importera la library \"time\", puis on utilisera la fonction \"time.time()\" préalablement et à l'issue du l'éxecuction de chacune des fonctions $\\textbf{TFD1}$ et $\\textbf{TFD2}$ " ] }, { "cell_type": "code", "execution_count": 10, "id": "855c687d-8987-43d8-9ae1-138c88c7da97", "metadata": {}, "outputs": [], "source": [ "import time " ] }, { "cell_type": "code", "execution_count": 11, "id": "ac9284d2-d239-47fc-8be7-fcfd991104b3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Time TDF1 0.07118105888366699\n" ] } ], "source": [ "N=400\n", "start=time.time()\n", "X1=TFD1(N)\n", "end=time.time()\n", "print(\"Time TFD1\",end-start)" ] }, { "cell_type": "code", "execution_count": 12, "id": "06d3b01e-18ff-4104-9a3a-08c3a6859ab5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Time TDF2 0.01265406608581543\n" ] } ], "source": [ "N=400\n", "start=time.time()\n", "X2=TFD2(N)\n", "end=time.time()\n", "print(\"Time TFD2\",end-start)" ] }, { "cell_type": "code", "execution_count": 15, "id": "b4a3c086-ce8d-4d76-a1df-1db34d220e05", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 66.4 ms, sys: 3.42 ms, total: 69.8 ms\n", "Wall time: 66.4 ms\n" ] } ], "source": [ "#Alternative\n", "N=400\n", "%time TFD1(N);" ] }, { "cell_type": "code", "execution_count": 16, "id": "6c52ef17-e6ee-4da6-a875-2078e8827b90", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 27.3 ms, sys: 12.5 ms, total: 39.8 ms\n", "Wall time: 10.5 ms\n" ] } ], "source": [ "#Alternative\n", "N=400\n", "%time TFD2(N);" ] }, { "cell_type": "markdown", "id": "63b3d1cc-8502-4261-aaf4-033c55dc07be", "metadata": {}, "source": [ "##### Q3.e. Que se passe-t-il lorsqu'on lance la fonction $\\textbf{TDF2}$ pour $N=50000$ ? " ] }, { "cell_type": "code", "execution_count": null, "id": "5ea265c7-633e-4562-be04-9a4594e3609a", "metadata": {}, "outputs": [], "source": [ "N=50000\n", "start=time.time()\n", "X2=TFD2(N)\n", "end=time.time()\n", "print(\"Time TFD2\",end-start)" ] }, { "cell_type": "markdown", "id": "90fa62b9-5dab-4f5b-a2b9-fbb4d8ef2ae0", "metadata": {}, "source": [ "# 2. FFT et \"débruitage\" d'un signal" ] }, { "cell_type": "markdown", "id": "21f91444-f6df-4bfa-bf37-776373661f96", "metadata": {}, "source": [ "Dans la pratique pour calculer efficacement la TFD d'un signal, on utilise l'algorithme de FFT. Dans la suite on va considérer cette manière très performante de calculer la TFD. L'algorithme de FFT est implémenté sous le nom \\texttt{fft}." ] }, { "cell_type": "markdown", "id": "695562be-dbc4-404c-8793-c5285e278dd4", "metadata": {}, "source": [ "## 2.1. Questions sur signal simple" ] }, { "cell_type": "markdown", "id": "968183bf-720d-48d9-96ae-d0fe28a5c54b", "metadata": {}, "source": [ "#### Soit un signal simple, défini par la fonction $T$-périodique (signal) $f$ avec $T=1$, $$f(x) = \\sin (2\\pi f_0 x) + \\sin(2 \\pi f_1 x), \\quad \\forall x \\in [0,T],$$ et pour lequel les fréquences $f_0=50$ et $f_1=120$ sont connues." ] }, { "cell_type": "markdown", "id": "34f63cba-82e6-4fcc-b72d-1d61ce1fec48", "metadata": {}, "source": [ "#### Q6 Représenter graphiquement le signal $f$ en utilisant $N=1000$ points. On notera $y$ le vecteur $y=f(t)$. " ] }, { "cell_type": "code", "execution_count": 31, "id": "266af1e3-7156-4268-964a-141feef9cfd6", "metadata": {}, "outputs": [], "source": [ "import numpy as np \n", "import matplotlib.pyplot as plt\n", "f0=50;\n", "f1=120;" ] }, { "cell_type": "code", "execution_count": 32, "id": "a2cb1940-c247-4786-9d07-50b3a8d0c852", "metadata": {}, "outputs": [], "source": [ "def signal (t):\n", " y=np.sin(2*np.pi*f0*t) + np.sin(2*np.pi*f1*t)\n", " return(y)" ] }, { "cell_type": "code", "execution_count": 33, "id": "80bc2657-a8df-445c-a170-ff97b395c38b", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 1000\n", "t = np.linspace(0, 1, N)\n", "y=signal(t)\n", "#print(t)\n", "#print(y)scaley: 'bool' = True\n", "plt.plot(t, y, '-b',linewidth = 0.3)\n", "plt.xlabel('t')\n", "plt.ylabel('f')\n", "plt.title(\"Fonction signal simple\")\n", "plt.grid() \n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c958a21c-27a6-4150-86be-96cfa24b0f57", "metadata": {}, "source": [ "#### Q7 TFD du vecteur $y$" ] }, { "cell_type": "markdown", "id": "97bb5295-d1e4-4a4f-b16e-8f407182323b", "metadata": {}, "source": [ "##### Q7.a. Calcul de la TFD de $y$ par la commande np.fft.fft(y). On la notera $\\text{fhat}$." ] }, { "cell_type": "code", "execution_count": 34, "id": "c2724736-b642-4cbd-aadd-12342095e27b", "metadata": {}, "outputs": [], "source": [ "fhat=np.fft.fft(y)" ] }, { "cell_type": "markdown", "id": "411fa1ea-e561-4e2e-8674-792fa94d928d", "metadata": {}, "source": [ "##### Q7.b. La TFD du signal $f$ calculée à partir de $y$, est le vecteur $Y$ constitué des nombres complexes $Y_n$, $n=0:N-1$. \n", "\n", "\n", "*remarque* On représente l'importance des fréquences du spectre du signal par le **spectre d'amplitude** qui correspond au module de la composante $n$ de $\\text{fhat}$ en fonction de la fréquence $n/T$ (pour tout $n=0,\\ldots,N-1$). \n", "\n", "Par ailleurs, par symétrie, voir la Section 3.2 du Chapitre 3 du cours, on représente généralement le spectre de puissance ou d'amplitude uniquement pour la première moitié des fréquences. \n", " " ] }, { "cell_type": "code", "execution_count": 37, "id": "61836d62-ae34-492b-8240-75d8e2ebcbc6", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#T=1\n", "spectre_amplitude=np.abs(fhat) # abs permet de calculer le module d'un nombre complexe\n", "F=np.arange(0,N) # fréquences en abscisses \n", "plt.plot(F,spectre_amplitude)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c5c2be0a-2533-4cae-bc59-4b00ab1e17f0", "metadata": {}, "source": [ "Par des considérations de symétrie de la DFT par rapport à sa $N/2$-e composante, on aurait pu tracer uniquement les $N/2$ premières composantes du spectre " ] }, { "cell_type": "code", "execution_count": 38, "id": "30eb9bde-d7c7-427d-8672-9cc634bbed7a", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N=1000\n", "L=np.arange(int(N/2))\n", "spectre_moit=abs(fhat[L]) # abs permet de calculer le module d'un nombre complexe\n", "plt.plot(L,spectre_moit,linewidth = 3,label='spectre de f'); # plot du spectre d'amplitude de f sur la première moitié des fréquences\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "eb7abdb2-48e2-477d-bea3-7a08c122bb14", "metadata": {}, "source": [ "## 2.2 Questions: débruitage du signal bruité " ] }, { "cell_type": "markdown", "id": "64b60ba1-f63c-41a7-a9eb-dadfe69d2cfd", "metadata": {}, "source": [ "### Q8 Ajouter un bruit Gaussien centré d'écart-type $2.5$ au signal simple $f$. On notera $funclean$ ce signal bruité. " ] }, { "cell_type": "code", "execution_count": 43, "id": "4eab637c-6607-43e1-a20c-851727b52cce", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import numpy.random as rd\n", "funclean=y+2.5*rd.randn(N)" ] }, { "cell_type": "markdown", "id": "13be839e-8d07-4c1e-bcf4-299598a9aa22", "metadata": {}, "source": [ "### Q9 Représenter sur la même fenêtre graphique le graphe de $f$ et celui de $funclean$. \n", "\n", "Dans le suite, on s'intéresse à débruiter $funclean$ pour retrouver $f$. " ] }, { "cell_type": "code", "execution_count": 46, "id": "16e683be-d061-43c7-b4e9-906b52f673df", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "\n", "plt.subplot(2,1,1)\n", "plt.plot(t,y,'-b',label='signal f'); # à la même échelle sur l'axe des ordonnées\n", "plt.ylim([-10, 10])\n", "\n", "plt.subplot(2,1,2)\n", "plt.plot(t,funclean,'-g',label='signal bruité');\n", "plt.ylim([-10, 10])\n", "plt.legend();\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "8a494ded-77b7-4474-b5ae-c340195a0870", "metadata": {}, "source": [ "### Q10 Calculer $funcleanhat$ la DFT de $funclean$, puis représenter sur une même fenêtre graphique les spectres d'amplitude de $fhat$ et $funcleanhat$" ] }, { "cell_type": "code", "execution_count": 48, "id": "ff55c060-21d1-4858-99e4-ea561457e3af", "metadata": {}, "outputs": [], "source": [ "N=1000\n", "L=np.arange(int(N/2))\n", "funclenahat=np.fft.fft(funclean)\n", "spectre_func_moit=abs(funclenahat[L])" ] }, { "cell_type": "code", "execution_count": 50, "id": "79a9f51f-7bc7-4a89-8aa7-60ccd7228fb2", "metadata": {}, "outputs": [ { "data": { "image/png": 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gUMdZQgghpqBeAcrs2bMxdOhQhIeHK2zPyspCXl4eIiIi2G18Ph8hISFISUkBAKSlpaGiokIhjUgkgq+vL5umNolEgqKiIoUHUdHEQ71QCCGEmACtm3gSEhJw+fJlpKamKu3Ly8sDAHh6eips9/T0ZDtO5eXlwcbGRqHmRZ5G/vraYmJisGLFCm2zavK4AhSqQSGEEGIKtKpByc7Oxrx587Br1y617Yy1e+4yDFNnb151aZYsWYLCwkL2kZ2drU22TRZXbQl1kiWEEGIKtApQ0tLSkJ+fj4CAAFhZWcHKygrJycn46quvYGVlxdac1K4Jyc/PZ/cJhUJIpVIUFBSoTFMbn8+Hs7OzwoOoGGZM8QkhhBAToFWAEhYWhoyMDKSnp7OPwMBATJw4Eenp6Wjbti2EQiGSkpLY10ilUiQnJ6NXr14AgICAAFhbWyukyc3NRWZmJpuGaIa7kyxFKIQQQoyfVn1QnJyc4Ovrq7DNwcEBbm5u7PbIyEhER0fDx8cHPj4+iI6Ohr29PSZMmAAAEAgEmDZtGhYsWAA3Nze4urpi4cKF8PPzU+p0S9Tjngel8fNBCCGE6JrOZ5JdvHgxxGIxZs2axU7UdvToUXYOFABYu3YtrKysMHbsWHaith07dtAcKFri6m9izjUoNIKJEEJMR4MDlFOnTik85/F4iIqKQlRUlMrX2NraIi4uDnFxcQ19e7PGdTk24/iEEEKICaEVnYyYjKOXrDnXIvBAyxkTQoipoADFiHGN4qF5UAghhJgCClCMGPc8KAbIiAFw9b8x59ojQggxNRSgGDHumWTN4yJtJqdJCCFmiwIUI8Y9zNg8rtzmEogRQoi5ogDFiHFdpM3lss11ntRJlhBCTAcFKEaM6yLNNbLHFHEHZ+Zx7oQQYg4oQDFiZl2DYi4nSgghZooCFCPGPZOsATJiABSgEEKIaaMAxYhRJ1lCCCGmigIUI8ZVW2Iu120KUAghxLRRgGLEzHmxQHNpyiKEEHNFAYoR46xBafxsGIbZnCghhJgnClCMmHnXoJjvNP+EEGIOKEAxYlzXY3O5SJtLIEYIIeaKAhQjxl2LYB4Xbq7mLR5NJEsIISaDAhQjxr1YYOPnwxBo1lhCCDFtFKAYMXPuh8E9B0zj54MQQoh+UIBixLhrUMzjKm0u50kIIeaKAhQjxtXMYc59UAghhJgOrQKUjRs3okuXLnB2doazszOCg4Nx+PBhdj/DMIiKioJIJIKdnR1CQ0Nx7do1hWNIJBLMnTsX7u7ucHBwwIgRI5CTk6ObszEzMpnyNnO5bnMFYtRJlhBCTIdWAYqXlxdWrVqFS5cu4dKlSxgwYABGjhzJBiGrV6/GmjVrsH79eqSmpkIoFGLgwIEoLi5mjxEZGYnExEQkJCTg7NmzKCkpwbBhw1BVVaXbMzMDXMGIuTR9UB8UQggxbVoFKMOHD8eQIUPQrl07tGvXDp9++ikcHR1x/vx5MAyDdevWYdmyZRgzZgx8fX0RHx+PsrIy7N69GwBQWFiIrVu3IjY2FuHh4ejWrRt27dqFjIwMHDt2TC8naMrMuZOsuQRihBBirurdB6WqqgoJCQkoLS1FcHAwsrKykJeXh4iICDYNn89HSEgIUlJSAABpaWmoqKhQSCMSieDr68um4SKRSFBUVKTwIKpmkjVARgzAXM6TEELMldYBSkZGBhwdHcHn8zFz5kwkJiaiU6dOyMvLAwB4enoqpPf09GT35eXlwcbGBi4uLirTcImJiYFAIGAfLVu21DbbJom7mcM8rtzmcp6EEGKutA5Q2rdvj/T0dJw/fx5vv/02pkyZguvXr7P7ebV6KjIMo7SttrrSLFmyBIWFhewjOztb22ybJHNeLJBqUAghxLRpHaDY2NjghRdeQGBgIGJiYuDv748vv/wSQqEQAJRqQvLz89laFaFQCKlUioKCApVpuPD5fHbkkPxBuIcZy8zkyk01KIQQYtoaPA8KwzCQSCTw9vaGUChEUlISu08qlSI5ORm9evUCAAQEBMDa2lohTW5uLjIzM9k0RHPmXIPCuVBio+eCEEKIvlhpk3jp0qUYPHgwWrZsieLiYiQkJODUqVM4cuQIeDweIiMjER0dDR8fH/j4+CA6Ohr29vaYMGECAEAgEGDatGlYsGAB3Nzc4OrqioULF8LPzw/h4eF6OUGTxtlJ1jwu01znaS7nTggh5kCrAOXRo0eYNGkScnNzIRAI0KVLFxw5cgQDBw4EACxevBhisRizZs1CQUEBgoKCcPToUTg5ObHHWLt2LaysrDB27FiIxWKEhYVhx44dsLS01O2ZmQHOGhQzuUZzTlJnJudOCCHmQKsAZevWrWr383g8REVFISoqSmUaW1tbxMXFIS4uTpu3Jhy450Exj6u0OZ87IYSYA1qLx4hxLxbY+PloKsz53AkhxNRQgGLEOGsRzKSrKPVBIYQQ00YBiokxl1oEc+5/Qwgh5oACFCNGa/HUvY0QQohxogDFiHHXIpjHRZpWMyaEENNGAYoR4+4kax5Xae6FEs3j3AkhxBxQgGLEzLuJR7NthBBCjBMFKCbGXC7SNA8KIYSYNgpQjBjXwoDmMsyYsw9K42eDEEKInlCAYsTMeagt9UEhhBDTRgGKEeOqLTGXizRnHxRzad8ihBAzQAGKETPnGhRz7iBMCCHmgAIUY2bGzRxcZ2ku504IIeaAAhQjxlmD0vjZMAjudYgIIYSYCgpQjJg5D7WlTrKEEGLaKEAxYpzNHLJGz4ZBcM+i2/j5IIQQoh8UoBgx7mYO87hKm/M6RIQQYg4oQDFmZlyLwL2asQEyQgghRC8oQDFi5jzUlqu2hGpQCCHEdFCAYsQ4p3s3k4s09UEhhBDTplWAEhMTgxdffBFOTk5o1qwZRo0ahZs3byqkYRgGUVFREIlEsLOzQ2hoKK5du6aQRiKRYO7cuXB3d4eDgwNGjBiBnJychp+NmeFe0dc8rtKqghFzCdAIIcTUaRWgJCcnY/bs2Th//jySkpJQWVmJiIgIlJaWsmlWr16NNWvWYP369UhNTYVQKMTAgQNRXFzMpomMjERiYiISEhJw9uxZlJSUYNiwYaiqqtLdmZkBc54LRFUgRrUohBBiGqy0SXzkyBGF59u3b0ezZs2QlpaGfv36gWEYrFu3DsuWLcOYMWMAAPHx8fD09MTu3bsxY8YMFBYWYuvWrfj2228RHh4OANi1axdatmyJY8eOYdCgQTo6NfNkLhdo1QEKA0vwGjk3hBBCdK1BfVAKCwsBAK6urgCArKws5OXlISIigk3D5/MREhKClJQUAEBaWhoqKioU0ohEIvj6+rJpapNIJCgqKlJ4EPOeqE0VMz99QggxGfUOUBiGwfz589GnTx/4+voCAPLy8gAAnp6eCmk9PT3ZfXl5ebCxsYGLi4vKNLXFxMRAIBCwj5YtW9Y32yaFu5Ns4+fDENTVoBBCCDF+9Q5Q5syZg6tXr2LPnj1K+3g8xSp2hmGUttWmLs2SJUtQWFjIPrKzs+ubbZPCPReIeVygVc2YayanTwghJq9eAcrcuXNx8OBBnDx5El5eXux2oVAIAEo1Ifn5+WytilAohFQqRUFBgco0tfH5fDg7Oys8iKrZVBs/H4ZANSiEEGLatApQGIbBnDlzsH//fpw4cQLe3t4K+729vSEUCpGUlMRuk0qlSE5ORq9evQAAAQEBsLa2VkiTm5uLzMxMNg3RlPnWoKg6S3M5f0IIMXVajeKZPXs2du/ejZ9++glOTk5sTYlAIICdnR14PB4iIyMRHR0NHx8f+Pj4IDo6Gvb29pgwYQKbdtq0aViwYAHc3Nzg6uqKhQsXws/Pjx3VQzTD1cxhLpdnVZ2BzeX8CSHE1GkVoGzcuBEAEBoaqrB9+/btmDp1KgBg8eLFEIvFmDVrFgoKChAUFISjR4/CycmJTb927VpYWVlh7NixEIvFCAsLw44dO2BpadmwszEzXAsDmssoHpUTtZnJas6EEGLqtApQNLn48Xg8REVFISoqSmUaW1tbxMXFIS4uTpu3J7VwzyTb+PkwBOqDQgghpo3W4jFi5jwPiqrTpACFEEJMAwUoxsyMa1BUBWLmcv6EEGLqKEAxYua9Fg/3dq5+OYQQQowPBShGjOtSbC5NPKqacszk9AkhxORRgGLEuDvJmscVmvqgEEKIaaMAxYhxd5I1QEYMQPUonkbOCCGEEL2gAMWYmXUnWe7tMnMpAEIIMXEUoBgxsx5mTJ1hCSHEpFGAYsS4YhEziU9U1hRRHxRCCDENFKAYMa6LsblcoKkPCiGEmDYKUIwY18XYXK7PNIqHEEJMGwUoRs18a1BUrmZsJudPCCGmjgIUI8bZnGEm12eVM8mayfkTQoipowDFiHHVFphLDQr1QSGEENNGAYoR455JtvHzYQg0iocQQkwbBShGjLuFx0wu0CprUMzk/AkhxMRRgGLEOJt4ZAbIiAFQHxRCCDFtFKAYMXOuLaDVjAkhxLRRgGLEuC7G5hK0UB8UQggxbVoHKKdPn8bw4cMhEonA4/Fw4MABhf0MwyAqKgoikQh2dnYIDQ3FtWvXFNJIJBLMnTsX7u7ucHBwwIgRI5CTk9OgEzFH5jyTrKq+NuZy/oQQYuq0DlBKS0vh7++P9evXc+5fvXo11qxZg/Xr1yM1NRVCoRADBw5EcXExmyYyMhKJiYlISEjA2bNnUVJSgmHDhqGqqqr+Z2KGzHktHtUzyTZuPgghhOiHlbYvGDx4MAYPHsy5j2EYrFu3DsuWLcOYMWMAAPHx8fD09MTu3bsxY8YMFBYWYuvWrfj2228RHh4OANi1axdatmyJY8eOYdCgQQ04HfPC3cTT+PkwBJnKEzWTAiCEEBOn0z4oWVlZyMvLQ0REBLuNz+cjJCQEKSkpAIC0tDRUVFQopBGJRPD19WXT1CaRSFBUVKTwIKqaM8zjAq26D0rj5oMQQoh+6DRAycvLAwB4enoqbPf09GT35eXlwcbGBi4uLirT1BYTEwOBQMA+WrZsqctsGy2ua7G5XKBV9kExlwIghBATp5dRPDweT+E5wzBK22pTl2bJkiUoLCxkH9nZ2TrLqzEz606yVINCCCEmTacBilAoBAClmpD8/Hy2VkUoFEIqlaKgoEBlmtr4fD6cnZ0VHsS8O8mqngfFTAqAEEJMnE4DFG9vbwiFQiQlJbHbpFIpkpOT0atXLwBAQEAArK2tFdLk5uYiMzOTTUM0Y86LBao6TfM4e0IIMX1aj+IpKSnB33//zT7PyspCeno6XF1d0apVK0RGRiI6Oho+Pj7w8fFBdHQ07O3tMWHCBACAQCDAtGnTsGDBAri5ucHV1RULFy6En58fO6qHaIazOcNMrtCqVzM2kwIghBATp3WAcunSJfTv3599Pn/+fADAlClTsGPHDixevBhisRizZs1CQUEBgoKCcPToUTg5ObGvWbt2LaysrDB27FiIxWKEhYVhx44dsLS01MEpmQ+ujqLmcoGmUTyEEGLatA5QQkND1bbz83g8REVFISoqSmUaW1tbxMXFIS4uTtu3JzVwLQxoLhdoVZ9BcwnQCCHE1NFaPEaMu4XHPC7QKvugUIBCCCEmgQIUI8bdSdYAGTEAWs2YEEJMGwUoRozzIm0mF2jqg0IIIaaNAhQjxr0Wj3lcoVU15UgqacFJQggxBRSgGDGznklWxfaCUmmj5oMQQoh+UIBixMx4GhSVgdhTClAIIcQkUIBixMx7qnvu7U9LKEAhhBBTQAGKEVPVD8MchtqqqkH5h2pQCCHEJFCAYsTMeSRLqaSSc/vTUkkj54QQQog+UIBixMx5PZqHz8Sc26kGhRBCTAMFKEZM9WyqjZuPxsYwDB4UcAco1AeFEEJMAwUoRsxc16MpEleiVMo930lBmRQyc2jjIoQQE0cBihEz18twzrMylftkDPBMXNGIuSGEEKIPFKAYMXPtg/LwWbna/U9KqKMsIYQYOwpQjJi5juJ5UKC6BgUAMh8UNlJOCCGE6AsFKEZMVUWJqdeg3MovUbv/7K0njZQTQggh+kIBipGSyRiUV3B3FL37pLSRc9N4qmQMjl5/pLCtucBW4fnpW09QZerVSIQQYuIoQDFSf+YVo0TFZGVX7j9r3Mw0ot9vP8XjYsU+Jp+O9lV4/qREgh8uZTdmtgghhOgYBShGKuW26maMK/cLGjEnjaeovAIrfr6msK2D0An92zeDbwtnhe2f/HIdyX89bszsEUII0SEKUIxQRZUMe9NyVO4/8Wc+istNZ6htRZUMx288wuivzyn1P3n1xZbg8Xh4/6WOCtvLpFWYsu0i/u9/KfjhUjZyCsrMYo0iQggxFVaGfPMNGzbg888/R25uLjp37ox169ahb9++hsxSkyWtlOHOkxKk33+G7y7cx595xSrTFpVXYtzm83g79HkEt3WDmyO/EXPaMIXiCjwoEOPBMzFuPy5BRk4hztx6jKJy5easTs2d8VrP1gCAPj7uGNOtBfZfeaCQJvVuAVLvVtcoOdta4YVmjmjj5gAPZz48HPnwcOJDYGcNR74V7G2s4Mi3ggPfEg58K/CtLMDj8fR/0oQQQpTwGAPdVn7//feYNGkSNmzYgN69e2PTpk345ptvcP36dbRq1Urta4uKiiAQCFBYWAhnZ2e1aTXFMAykVTJUyRhUyRjIZEClTIYqhlHaJmMYVHJtq2JQxShvkzEMqlRsk1ZWQVwhg1haCXFFVfVDKoO4ohLF5ZV4XCzB42IJ/imTqhy10+I5O3g683FZRd8TNwcbeLnao8VzthDYWcPZ1hrOdtZwtrWCnU31hZhvZQG+tSX7f9t//29jZQErCwtY8ADwAAseDzKGgbRSBmmlDBKlf6uUnksqZZBWySCpqP5XLK1CcXklisorUCiuQJG4AsXllXhWJlU5Q2xt7o58JLzVEy80c2S3SStlmLvnMn679kjNKzVnwQOsLavLwObff61r/WtjyasuH4vqsrG04MGSx4MF+6+q7TxY8ABLC95/+y144PEAHuT/Quk5eDx2u0WN/8sDKbWvr5ke/z7nOG7N11v8+x95ermaYVvNGE7h/wqpFPcpbtfguDX2KG5XdXxN0jfgfBpyTBV5q/0aqCivutQud61e24B4vCGhfENuBAyX5wa82AB/o/q+o7WlBXxbCOr5amXaXL8NFqAEBQWhe/fu2LhxI7utY8eOGDVqFGJiYtS+Vh8BypX7BRi9IUUnx2pMNlYWSHirJ9wd+Bj61RkUq+g4a0p8Wzhj/fjuaOPuoLRPJmPw3cX7iDt+C/nFNGEbIYQ0hEhgi5QlYTo7njbXb4M08UilUqSlpeH9999X2B4REYGUFOUgQSKRQCL572JTVFSk8zxZWhhfVX4rV3usGeuP7q1cAAB73uqJObsv4+5T9ROZGasuXgJM6tkao7u1gJUld/cpCwseJvVsjVcDW+JwZi6OZObh9ztP8azMdPrkEEKIOTBIgPLkyRNUVVXB09NTYbunpyfy8vKU0sfExGDFihV6zZOxBCgtnrND15bP4SVfIQZ1FsLG6r8LtW8LAY5E9sNP6Q9wKCMPl+7+gzINm0yammZOfHi52KFDc2d0aSFASHsPNBfYafx6GysLjOzaAiO7toBMxiCnoLpPy+3HJXj4rByPSyR4XFyOJyVSlJRXolRSiRJppcmvBE0IIcbCoJ1ka7c7MgzD2Ra5ZMkSzJ8/n31eVFSEli1b6jQv9QlQrCz+61Mg/7/Cv//2LeDaJn9YW/Jgb2MFO2tL2Fpbws7GAvY2VrC1toSDjSXc/+3I6eHEh+g5OwjsrNXmydbaEq++2AqvvtgKFVUy3H1SiuyCMmT/I8bTEkl1n4/ySrbvh6RShvKK6n4i8v4ikgoZyiurNLpY83io7qtiWd2Hpfrff59bWYBvZQmbf/u12Pz74FtZKPSDcbazhsDOGk621mjmxEfz52zBt7LU+u+hioUFD63c7NHKzR79OzRTmY5hGIgrqlAiqUSppArlFdX9aSqqqvvTSKtkqKhiFLZJqmSoqpKhiql+fZVM3g+puo8R+/9//5X3PZIppa3+P/PvcRhUzxTM4L/nYAAG8jTV/5cx8hmFGaX0NZ/j3+cy+XvUSI9azznfv8ZngamxTKXCdoU0iuWqusw1OK6KYykcVcv02p6PYp4bcEwV6WvvrW+g3JD4uiGt/Q1734a81jB5bsiLDfE3ash72tro7rdYWwYJUNzd3WFpaalUW5Kfn69UqwIAfD4ffL5+R6J4uzvg5MJQpWCCDUI4tjV11pYW8PF0go+nk9avZf7tCFxeUfXvRZBhL3A8Hq9GB1qeyYx04fGqg0V7GytA+yIjhBCiQwYJUGxsbBAQEICkpCSMHj2a3Z6UlISRI0caIkvgW1nCm6PTpbni8aprd6xV9PUghBBC9MlgTTzz58/HpEmTEBgYiODgYGzevBn379/HzJkzDZUlQgghhDQRBgtQXn31VTx9+hQff/wxcnNz4evri19//RWtW7c2VJYIIYQQ0kQYbB6UhtDHPCiEEEII0a8mPw9KQ8ljKn3Mh0IIIYQQ/ZBftzWpGzHKAKW4uHodGl0PNSaEEEKI/hUXF0MgUD+FvlE28chkMjx8+BBOTk46H+Iqn2MlOzubmo/0iMq58VBZNw4q58ZB5dx49FHWDMOguLgYIpEIFhbqR4kaZQ2KhYUFvLy89Poezs7O9OFvBFTOjYfKunFQOTcOKufGo+uyrqvmRI4muSCEEEJIk0MBCiGEEEKaHApQauHz+Vi+fLnep9Y3d1TOjYfKunFQOTcOKufGY+iyNspOsoQQQggxbVSDQgghhJAmhwIUQgghhDQ5FKAQQgghpMmhAIUQQgghTQ4FKDVs2LAB3t7esLW1RUBAAM6cOWPoLBmd06dPY/jw4RCJRODxeDhw4IDCfoZhEBUVBZFIBDs7O4SGhuLatWsKaSQSCebOnQt3d3c4ODhgxIgRyMnJacSzaNpiYmLw4osvwsnJCc2aNcOoUaNw8+ZNhTRUzrqxceNGdOnShZ2oKjg4GIcPH2b3UznrR0xMDHg8HiIjI9ltVNYNFxUVBR6Pp/AQCoXs/iZXxgxhGIZhEhISGGtra2bLli3M9evXmXnz5jEODg7MvXv3DJ01o/Lrr78yy5YtY/bt28cAYBITExX2r1q1inFycmL27dvHZGRkMK+++irTvHlzpqioiE0zc+ZMpkWLFkxSUhJz+fJlpn///oy/vz9TWVnZyGfTNA0aNIjZvn07k5mZyaSnpzNDhw5lWrVqxZSUlLBpqJx14+DBg8yhQ4eYmzdvMjdv3mSWLl3KWFtbM5mZmQzDUDnrw8WLF5k2bdowXbp0YebNm8dup7JuuOXLlzOdO3dmcnNz2Ud+fj67v6mVMQUo/+rRowczc+ZMhW0dOnRg3n//fQPlyPjVDlBkMhkjFAqZVatWsdvKy8sZgUDA/O9//2MYhmGePXvGWFtbMwkJCWyaBw8eMBYWFsyRI0caLe/GJD8/nwHAJCcnMwxD5axvLi4uzDfffEPlrAfFxcWMj48Pk5SUxISEhLABCpW1bixfvpzx9/fn3NcUy5iaeABIpVKkpaUhIiJCYXtERARSUlIMlCvTk5WVhby8PIVy5vP5CAkJYcs5LS0NFRUVCmlEIhF8fX3pb6FCYWEhAMDV1RUAlbO+VFVVISEhAaWlpQgODqZy1oPZs2dj6NChCA8PV9hOZa07t27dgkgkgre3N8aNG4c7d+4AaJplbJSLBerakydPUFVVBU9PT4Xtnp6eyMvLM1CuTI+8LLnK+d69e2waGxsbuLi4KKWhv4UyhmEwf/589OnTB76+vgConHUtIyMDwcHBKC8vh6OjIxITE9GpUyf2B5nKWTcSEhJw+fJlpKamKu2jz7RuBAUFYefOnWjXrh0ePXqElStXolevXrh27VqTLGMKUGrg8XgKzxmGUdpGGq4+5Ux/C25z5szB1atXcfbsWaV9VM660b59e6Snp+PZs2fYt28fpkyZguTkZHY/lXPDZWdnY968eTh69ChsbW1VpqOybpjBgwez//fz80NwcDCef/55xMfHo2fPngCaVhlTEw8Ad3d3WFpaKkWA+fn5StEkqT95b3F15SwUCiGVSlFQUKAyDak2d+5cHDx4ECdPnoSXlxe7ncpZt2xsbPDCCy8gMDAQMTEx8Pf3x5dffknlrENpaWnIz89HQEAArKysYGVlheTkZHz11VewsrJiy4rKWrccHBzg5+eHW7duNcnPMwUoqP4BCggIQFJSksL2pKQk9OrVy0C5Mj3e3t4QCoUK5SyVSpGcnMyWc0BAAKytrRXS5ObmIjMzk/4W/2IYBnPmzMH+/ftx4sQJeHt7K+ynctYvhmEgkUionHUoLCwMGRkZSE9PZx+BgYGYOHEi0tPT0bZtWyprPZBIJLhx4waaN2/eND/POu92a6Tkw4y3bt3KXL9+nYmMjGQcHByYu3fvGjprRqW4uJi5cuUKc+XKFQYAs2bNGubKlSvscO1Vq1YxAoGA2b9/P5ORkcGMHz+ecxibl5cXc+zYMeby5cvMgAEDaKhgDW+//TYjEAiYU6dOKQwXLCsrY9NQOevGkiVLmNOnTzNZWVnM1atXmaVLlzIWFhbM0aNHGYahctanmqN4GIbKWhcWLFjAnDp1irlz5w5z/vx5ZtiwYYyTkxN7nWtqZUwBSg1ff/0107p1a8bGxobp3r07O2yTaO7kyZMMAKXHlClTGIapHsq2fPlyRigUMnw+n+nXrx+TkZGhcAyxWMzMmTOHcXV1Zezs7Jhhw4Yx9+/fN8DZNE1c5QuA2b59O5uGylk33njjDfY3wcPDgwkLC2ODE4ahctan2gEKlXXDyec1sba2ZkQiETNmzBjm2rVr7P6mVsY8hmEY3dfLEEIIIYTUH/VBIYQQQkiTQwEKIYQQQpocClAIIYQQ0uRQgEIIIYSQJocCFEIIIYQ0ORSgEEIIIaTJoQCFEEIIIU0OBSiEEEIIaXIoQCGEEEJIk0MBCiGEEEKaHCtDZ6A+ZDIZHj58CCcnJ/B4PENnhxBCCCEaYBgGxcXFEIlEsLBQX0dilAHKw4cP0bJlS0NngxBCCCH1kJ2dDS8vL7VpjDJAcXJyAlB9gs7OzgbODSGEEEI0UVRUhJYtW7LXcXWMMkCRN+s4OztTgEIIIYQYGU26Z1AnWUIIIYQ0ORSgEEIIIaTJoQCFGDVJpQT/iP8BwzCGzgohhBAdMso+KIQAQMajDAzfMxz3Cu9hVIdR+OGVH2BtaW3obBFSp6qqKlRUVBg6G4TohY2NTZ1DiDVBAQoxWlHJUbhXeA8AcODPA/j11q8Y2WGkgXNFiGoMwyAvLw/Pnj0zdFYI0RsLCwt4e3vDxsamQcehAIUYrf039is8//DkhxSgkCZNHpw0a9YM9vb2NNEkMTnyiVRzc3PRqlWrBn3GKUAhhJBGUFVVxQYnbm5uhs4OIXrj4eGBhw8forKyEtbW9W92p06yhBDSCOR9Tuzt7Q2cE0L0S960U1VV1aDjaBWgREVFgcfjKTyEQiG7n2EYREVFQSQSwc7ODqGhobh27ZrCMSQSCebOnQt3d3c4ODhgxIgRyMnJadBJEEKIsaBmHWLqdPUZ17oGpXPnzsjNzWUfGRkZ7L7Vq1djzZo1WL9+PVJTUyEUCjFw4EAUFxezaSIjI5GYmIiEhAScPXsWJSUlGDZsWIMjLUIIIYSYDq0DFCsrKwiFQvbh4eEBoLr2ZN26dVi2bBnGjBkDX19fxMfHo6ysDLt37wYAFBYWYuvWrYiNjUV4eDi6deuGXbt2ISMjA8eOHdPtmRGzw4DmQiGENFxoaCgiIyMbdIy8vDwMHDgQDg4OeO6553SSL020adMG69ata7T30yetA5Rbt25BJBLB29sb48aNw507dwAAWVlZyMvLQ0REBJuWz+cjJCQEKSkpAIC0tDRUVFQopBGJRPD19WXTEEIIIXJTp07FqFGjDJ0Nra1duxa5ublIT0/HX3/9ZejsGCWtRvEEBQVh586daNeuHR49eoSVK1eiV69euHbtGvLy8gAAnp6eCq/x9PTEvXvVc1Xk5eXBxsYGLi4uSmnkr+cikUggkUjY50VFRdpk26QxDINf/voFZRVlGNNxDE1URggxSxUVFQ0aMaJrt2/fRkBAAHx8fAydFaOlVQ3K4MGD8fLLL8PPzw/h4eE4dOgQACA+Pp5NU7tzDMMwdXaYqStNTEwMBAIB+2jZsqU22TZp847Mw4iEERi3bxyG7xlu6OwYFE13T4yFjJHhceljgz5kjEyjvO7duxd+fn6ws7ODm5sbwsPDUVpaCuC/2o0VK1agWbNmcHZ2xowZMyCVStnXMwyD1atXo23btrCzs4O/vz/27t2r8B7Xrl3D0KFD4ezsDCcnJ/Tt2xe3b99GVFQU4uPj8dNPP7EDM06dOoW7d++Cx+Phhx9+QGhoKGxtbbFr1y4AwPbt29GxY0fY2tqiQ4cO2LBhg9rzKy0txeTJk+Ho6IjmzZsjNjZWKY1UKsXixYvRokULODg4ICgoCKdOnVJ5zDZt2mDfvn3YuXMneDwepk6dyuY5PT2dTffs2TP2nADg1KlT4PF4OH78OAIDA2Fvb49evXrh5s2bCsc/ePAgAgMDYWtrC3d3d4wZM0ZlXgoLC/HWW2+xf58BAwbgjz/+YPffvn0bI0eOhKenJxwdHfHiiy8qdblo06YNoqOj8cYbb8DJyQmtWrXC5s2b1ZSqbjRoHhQHBwf4+fnh1q1bbBVcXl4emjdvzqbJz89na1WEQiGkUikKCgoUalHy8/PRq1cvle+zZMkSzJ8/n31eVFREQQqqf+TiLsaxz3+7/Rv+fPInOrh3MGCuCCF1eVr2FM2+aGbQPOQvzIeHg4faNLm5uRg/fjxWr16N0aNHo7i4GGfOnFG4GTh+/DhsbW1x8uRJ3L17F6+//jrc3d3x6aefAgA++OAD7N+/Hxs3boSPjw9Onz6N1157DR4eHggJCcGDBw/Qr18/hIaG4sSJE3B2dsa5c+dQWVmJhQsX4saNGygqKsL27dsBAK6urnj48CEA4L333kNsbCy2b98OPp+PLVu2YPny5Vi/fj26deuGK1euYPr06XBwcMCUKVM4z3HRokU4efIkEhMTIRQKsXTpUqSlpaFr165smtdffx13795FQkICRCIREhMT8dJLLyEjI4OzhiQ1NRWTJ0+Gs7MzvvzyS9jZ2aGgoEDjv82yZcsQGxsLDw8PzJw5E2+88QbOnTsHADh06BDGjBmDZcuW4dtvv4VUKmUrC2pjGAZDhw6Fq6srfv31VwgEAmzatAlhYWH466+/4OrqipKSEgwZMgQrV66Era0t4uPjMXz4cNy8eROtWrVijxUbG4tPPvkES5cuxd69e/H222+jX79+6NBBf9ebBgUoEokEN27cQN++feHt7Q2hUIikpCR069YNQHXUmZycjM8++wwAEBAQAGtrayQlJWHs2LEAqr8AmZmZWL16tcr34fP54PP5DcmqSaqSKY98uvnkJgUohBCdyM3NRWVlJcaMGYPWrVsDAPz8/BTS2NjYYNu2bbC3t0fnzp3x8ccfY9GiRfjkk08gFouxZs0anDhxAsHBwQCAtm3b4uzZs9i0aRNCQkLw9ddfQyAQICEhgW2iadeuHXt8Ozs7SCQShSkt5CIjIxVqDz755BPExsay27y9vXH9+nVs2rSJM0ApKSnB1q1bsXPnTgwcOBBAdYuAl5cXm+b27dvYs2cPcnJyIBKJAAALFy7EkSNHsH37dkRHRysd18PDA3w+H3Z2dmy+tQlQPv30U4SEhAAA3n//fQwdOhTl5eWwtbXFp59+inHjxmHFihVsen9/f87jnDx5EhkZGcjPz2evoV988QUOHDiAvXv34q233oK/v7/C61euXInExEQcPHgQc+bMYbcPGTIEs2bNAlAdGK5duxanTp1qOgHKwoULMXz4cLRq1Qr5+flYuXIlioqKMGXKFPB4PERGRiI6Oho+Pj7w8fFBdHQ07O3tMWHCBACAQCDAtGnTsGDBAri5ucHV1RULFy5km4yIdmjUiiIqD0J0y9/fH2FhYfDz88OgQYMQERGBV155RaEG3N/fX2HyueDgYJSUlCA7Oxv5+fkoLy9nL/5yUqmUvZFNT09H375969V/JDAwkP3/48ePkZ2djWnTpmH69Ons9srKSggEAs7X3759G1KplA2egOoamvbt27PPL1++DIZhFIImoPoGXV8zAnfp0oX9v7xFIj8/H61atUJ6errC+amTlpaGkpISpXyKxWLcvn0bQHUT14oVK/DLL7+ws7+KxWLcv39fZZ7kc6Dl5+fX6/w0pVWAkpOTg/Hjx+PJkyfw8PBAz549cf78eTayXrx4McRiMWbNmoWCggIEBQXh6NGjcHJyYo+xdu1aWFlZYezYsRCLxQgLC8OOHTtgaWmp2zMzA5q2IRNCSH1YWloiKSkJKSkpOHr0KOLi4rBs2TJcuHAB3t7eal/L4/Egk1X/Rh06dAgtWrRQ2C+/o7ezs6t3/hwcHNj/y99ry5YtCAoKUjoPLpr0W5PJZLC0tERaWprScRwdHTXOq3x135rvqWpF65rBmrx/pvz8tCkvmUyG5s2bc/aXkQ99XrRoEX777Td88cUXeOGFF2BnZ4dXXnlFoR9R7TzJ8yXPk75oFaAkJCSo3c/j8RAVFYWoqCiVaWxtbREXF4e4uDiVaYhmuAIUc65FoE6yxFi42bshf6F+7z41yYMmeDweevfujd69e+Ojjz5C69atkZiYyPYL/OOPPyAWi9kL5/nz5+Ho6AgvLy+4uLiAz+fj/v37bJNFbV26dEF8fLzKUTg2NjYaTeTp6emJFi1a4M6dO5g4caJG5/bCCy/A2toa58+fZ/tbFBQU4K+//mLz261bN1RVVSE/Px99+/bV6Lhc5HOG5ebmKtQeaatLly44fvw4Xn/99TrTdu/eHXl5ebCyskKbNm0405w5cwZTp07F6NGjAVQ3e929e1frfOkDLRZoxKgGhRDjZMGzqLODalNw4cIFHD9+HBEREWjWrBkuXLiAx48fo2PHjmwaqVSKadOm4YMPPsC9e/ewfPlyzJkzBxYWFnBycsLChQvx7rvvQiaToU+fPigqKkJKSgocHR0xZcoUzJkzB3FxcRg3bhyWLFkCgUCA8+fPo0ePHmjfvj3atGmD3377DTdv3oSbm5vK5hqgejmWd955B87Ozhg8eDAkEgkuXbqEgoIChYEWco6Ojpg2bRoWLVoENzc3eHp6YtmyZWxtB1DdH2bixImYPHkyYmNj0a1bNzx58gQnTpyAn58fhgwZolFZ2tnZoWfPnli1ahXatGmDJ0+e4IMPPtDir1Ft+fLlCAsLw/PPP49x48ahsrIShw8fxuLFi5XShoeHIzg4GKNGjcJnn32G9u3b4+HDh/j1118xatQoBAYG4oUXXsD+/fsxfPhw8Hg8fPjhh3qvGdEUBShGjAIURbTGCSG65ezsjNOnT2PdunUoKipC69atERsbi8GDB7NpwsLC4OPjg379+kEikWDcuHEKteiffPIJmjVrhpiYGNy5cwfPPfccunfvjqVLlwIA3NzccOLECSxatAghISGwtLRE165d0bt3bwDA9OnTcerUKQQGBqKkpAQnT55UWRvw5ptvwt7eHp9//jkWL17MjjRVNyvs559/jpKSEowYMQJOTk5YsGABCgsLFdJs374dK1euxIIFC/DgwQO4ubkhODhY4+BEbtu2bXjjjTcQGBiI9u3bY/Xq1QoTl2oiNDQUP/74Iz755BOsWrUKzs7O6NevH2daHo+HX3/9FcuWLcMbb7yBx48fQygUol+/fuzo2rVr1+KNN95Ar1694O7ujvfee6/JzDXGY4ywXryoqAgCgQCFhYVwdnY2dHYM5ln5M7h8pjjpXeKriRjVYZRhMtTIeCsUA5KO7h1xffZ1A+WGEPXKy8uRlZUFb29v2NraGjo7OjF16lQ8e/YMBw4cMHRWSBOi7rOuzfVb66nuSdNBNSiEEEJMFQUoRowCFEIIIaaK+qAYMQpQFJnzCCZCDGHHjh2GzgIxYVSDYsQoQCGEEGKqKEAxYhSgKDLC/t6EEEJUoADFiFGAQojxaSpzTBCiL7q6WaQ+KEaMAhRCjIeNjQ0sLCzw8OFDeHh4wMbGhubuISaHYRg8fvwYPB6vXusr1UQBihGjAEURdZIlTZmFhQW8vb2Rm5uLhw8fGjo7hOgNj8eDl5dXg9fYowDFiFGAQohxsbGxQatWrVBZWanR+jKEGCNra2udLABMAYoRowCFEOMjr/puaPU3IaaOOskaMQpQCCGEmCoKUIwYBSiEEEJMFQUoRowrQDHnuUDM+dwJIcTUUIBixDgDFBrJQgghxARQgGLEuAIUavYhhBBiCihAMWIUoCii2iNCCDEdDQpQYmJiwOPxEBkZyW5jGAZRUVEQiUSws7NDaGgorl27pvA6iUSCuXPnwt3dHQ4ODhgxYgRycnIakhWzxBWMVMlobgVCCCHGr94BSmpqKjZv3owuXboobF+9ejXWrFmD9evXIzU1FUKhEAMHDkRxcTGbJjIyEomJiUhISMDZs2dRUlKCYcOG0cRFWqIaFEIIIaaqXgFKSUkJJk6ciC1btsDFxYXdzjAM1q1bh2XLlmHMmDHw9fVFfHw8ysrKsHv3bgBAYWEhtm7ditjYWISHh6Nbt27YtWsXMjIycOzYMd2clZmgAEURjeIhhBDTUa8AZfbs2Rg6dCjCw8MVtmdlZSEvLw8RERHsNj6fj5CQEKSkpAAA0tLSUFFRoZBGJBLB19eXTVObRCJBUVGRwoNQgEIIIcR0aT3VfUJCAi5fvozU1FSlfXl5eQAAT09Phe2enp64d+8em8bGxkah5kWeRv762mJiYrBixQpts2ryKEBRRJ1kCSHEdGhVg5KdnY158+Zh165dsLW1VZmu9hLiDMPUuay4ujRLlixBYWEh+8jOztYm2ybLnAMUas4hhBDTplWAkpaWhvz8fAQEBMDKygpWVlZITk7GV199BSsrK7bmpHZNSH5+PrtPKBRCKpWioKBAZZra+Hw+nJ2dFR7EzAMUjtoSHtQHwYQQQoyHVgFKWFgYMjIykJ6ezj4CAwMxceJEpKeno23bthAKhUhKSmJfI5VKkZycjF69egEAAgICYG1trZAmNzcXmZmZbBqiGXMOUGgWXUIIMW1a9UFxcnKCr6+vwjYHBwe4ubmx2yMjIxEdHQ0fHx/4+PggOjoa9vb2mDBhAgBAIBBg2rRpWLBgAdzc3ODq6oqFCxfCz89PqdMtUY8CFEIIIaZK606ydVm8eDHEYjFmzZqFgoICBAUF4ejRo3BycmLTrF27FlZWVhg7dizEYjHCwsKwY8cOWFpa6jo7Js2cAxTqg0IIIaatwQHKqVOnFJ7zeDxERUUhKipK5WtsbW0RFxeHuLi4hr69WTPnAIVWciaEENNGa/EYMXMOUKi/CSGEmDYKUIyYOQco1EmWEEJMGwUoRowCFEIIIaaKAhQjZs4BCvU3IYQQ00YBihEz5wCFOskSQohpowDFiFGAQgghxFRRgGLEzDlAoQ6xhBBi2ihAMWLmHKCYy3kSQoi5ogDFiFGAQgghxFRRgGLEuC7SVUyVAXLS+KhDLCGEmDYKUIwY1aAoon4phBBiOihAMWLmHKBQMEIIIaaNAhQjZs4BCs2DQgghpo0CFCNGAQohhBBTRQGKETPnAIVqSwghxLRRgGLEzDlAoU6yhBBi2ihAMWIUoBBCCDFVFKAYMXMOUKi2hBBCTJtWAcrGjRvRpUsXODs7w9nZGcHBwTh8+DC7n2EYREVFQSQSwc7ODqGhobh27ZrCMSQSCebOnQt3d3c4ODhgxIgRyMnJ0c3ZmBlzDlDM5TwJIcRcaRWgeHl5YdWqVbh06RIuXbqEAQMGYOTIkWwQsnr1aqxZswbr169HamoqhEIhBg4ciOLiYvYYkZGRSExMREJCAs6ePYuSkhIMGzYMVVXmMQOqLplzgEKdZAkhxLRpFaAMHz4cQ4YMQbt27dCuXTt8+umncHR0xPnz58EwDNatW4dly5ZhzJgx8PX1RXx8PMrKyrB7924AQGFhIbZu3YrY2FiEh4ejW7du2LVrFzIyMnDs2DG9nKApM+cAheZBIYQQ01bvPihVVVVISEhAaWkpgoODkZWVhby8PERERLBp+Hw+QkJCkJKSAgBIS0tDRUWFQhqRSARfX182DReJRIKioiKFB6EARZNthBBCjJPWAUpGRgYcHR3B5/Mxc+ZMJCYmolOnTsjLywMAeHp6KqT39PRk9+Xl5cHGxgYuLi4q03CJiYmBQCBgHy1bttQ22ybJnC/SXJ1kzeXcCSHEHGgdoLRv3x7p6ek4f/483n77bUyZMgXXr19n9/N4PIX0DMMobautrjRLlixBYWEh+8jOztY22ybJnAMUcz53QggxB1oHKDY2NnjhhRcQGBiImJgY+Pv748svv4RQKAQApZqQ/Px8tlZFKBRCKpWioKBAZRoufD6fHTkkfxDzvkib87kTQog5aPA8KAzDQCKRwNvbG0KhEElJSew+qVSK5ORk9OrVCwAQEBAAa2trhTS5ubnIzMxk0xDNmfNFmqtDrLmcOyGEmAMrbRIvXboUgwcPRsuWLVFcXIyEhAScOnUKR44cAY/HQ2RkJKKjo+Hj4wMfHx9ER0fD3t4eEyZMAAAIBAJMmzYNCxYsgJubG1xdXbFw4UL4+fkhPDxcLydoysw5QDHncyeEEHOgVYDy6NEjTJo0Cbm5uRAIBOjSpQuOHDmCgQMHAgAWL14MsViMWbNmoaCgAEFBQTh69CicnJzYY6xduxZWVlYYO3YsxGIxwsLCsGPHDlhaWur2zMyAOV+kzfncCSHEHGgVoGzdulXtfh6Ph6ioKERFRalMY2tri7i4OMTFxWnz1oSDOV+kaRQPIYSYNlqLx4iZc4BizudOCCHmgAIUI8Z1Qa5izGPJAOokSwghpo0CFCNmzrUI5nzuhBBiDihAMWLmfJHmXIuHo18KIYQQ40QBihEz5wCFOskSQohpowDFiJlzgGLO504IIeaAAhQjZs4XaVXnydV5lhBCiPGhAMWImXOAoioQMZfzJ4QQU0cBihEz5wBF1Xmay/kTQoipowDFiJlzgKJqxI65nD8hhJg6ClCMmDkHKFSDQgghpo0CFCNGAYrm2wkhhBgXClCMmDkHKNRJlhBCTBsFKEbMnAMUqkEhhBDTRgGKEaMARfPthBBCjAsFKEbMnAMUVaN4aD0eQggxDRSgGDFzDlCoBoUQQkwbBShGrIqpUtpmLhdoClAIIcS0aRWgxMTE4MUXX4STkxOaNWuGUaNG4ebNmwppGIZBVFQURCIR7OzsEBoaimvXrimkkUgkmDt3Ltzd3eHg4IARI0YgJyen4WdjZsy5BoVG8RBCiGnTKkBJTk7G7Nmzcf78eSQlJaGyshIREREoLS1l06xevRpr1qzB+vXrkZqaCqFQiIEDB6K4uJhNExkZicTERCQkJODs2bMoKSnBsGHDUFWlXCNAVDPnAEXVeS47vqyRc0IIIUQftApQjhw5gqlTp6Jz587w9/fH9u3bcf/+faSlpQGovqtdt24dli1bhjFjxsDX1xfx8fEoKyvD7t27AQCFhYXYunUrYmNjER4ejm7dumHXrl3IyMjAsWPHdH+GJsycAxRVnWG3pW/Dg6IHjZwbQgghutagPiiFhYUAAFdXVwBAVlYW8vLyEBERwabh8/kICQlBSkoKACAtLQ0VFRUKaUQiEXx9fdk0tUkkEhQVFSk8CHcwUiUzj1oodYHYnsw9jZgTQggh+lDvAIVhGMyfPx99+vSBr68vACAvLw8A4OnpqZDW09OT3ZeXlwcbGxu4uLioTFNbTEwMBAIB+2jZsmV9s91kMAyDY3eOIel2ksr+FHUx5xoUdecprZI2Yk4IIYToQ70DlDlz5uDq1avYs0f5bpXH4yk8ZxhGaVtt6tIsWbIEhYWF7CM7O7u+2W4yZvwyAwO/HYiIXRGY8cuMeh3DnAMUdUEdBSiEEHNQJCnC4qTFeOvnt/D3P38bOjs6V68AZe7cuTh48CBOnjwJLy8vdrtQKAQApZqQ/Px8tlZFKBRCKpWioKBAZZra+Hw+nJ2dFR7GrEBcgC2Xt7DPt1zegn/E/2h9HHMOUKgGhRBi7qYemIrPUz7Hlstb0G97P5Nr4tcqQGEYBnPmzMH+/ftx4sQJeHt7K+z39vaGUChEUlISu00qlSI5ORm9evUCAAQEBMDa2lohTW5uLjIzM9k0pu5BsXInzofFD7U+DgUo3CqqKhoxJ8TQGIZBWUWZ2Xz2CZFL/DOR/X9uSS4O3TpkwNzonlYByuzZs7Fr1y7s3r0bTk5OyMvLQ15eHsRiMYDqpp3IyEhER0cjMTERmZmZmDp1Kuzt7TFhwgQAgEAgwLRp07BgwQIcP34cV65cwWuvvQY/Pz+Eh4fr/gxNmDkHKOqmtKcaFPNRWF6I8G/D4RDtgKBvgpBbnGvoLOlNTlEOBu0aBO8vvfH5uc8NnR1iYFzN3NmFxt/9oSatApSNGzeisLAQoaGhaN68Ofv4/vvv2TSLFy9GZGQkZs2ahcDAQDx48ABHjx6Fk5MTm2bt2rUYNWoUxo4di969e8Pe3h4///wzLC0tdXdmZsCcAxR15/nVxa9w+t7pRswNMZSEzAScyDoBALj08JJC06mpiToVhaO3j+Lus7tYfGwxMvMzDZ0lYkBcM4mb2s2Z1k08XI+pU6eyaXg8HqKiopCbm4vy8nIkJyezo3zkbG1tERcXh6dPn6KsrAw///yzSYzMaWzmHKDUNfJp+s/T6z06ihiPmYdmKjxffmq5gXKif1uvbFV4/nHyxwbKCWkKuIKRCplpNW/TWjwGwNVHolJWqfVxzDlAqes8/3r6F0orStWmIcSYFUoKDZ0FYkBc1xFT639HAYoBcEW59amaowBFvbKKskbICSGGwYP6qRuIaaMaFKIXnB+sekS+5hygqOskK1cq1a4GRVwhxocnPsTrP72OK7lX6ps1QogaT8qeYHHSYiw5tgQF4oK6X0A4cQUjplaDYmXoDJgjrg8R1aBoRx81KO/+9i42pW0CAOy9vhcP5j+AM9+459whpquuyS+bqsHfDcalh5cAACk5KUiemmzgHBknziYeqkEhDaWrqjkKUNTTtg+KPDgBgBJpCTakbgBQvb7R3Wd3ta6RIUSfjK2Jp1JWiUVHF7HBCQCcvnca+aX5BsyV8dJVTXxTRgGKAVAflIbTZIROQwOK9Lx0lEpLEbIjBN5feqP9+vbIeJTRoGPWx+/Zv8P7S284RDtgze9rGv39ieGZwoi0Bb8twBe/f6G0vbCcOvvWh66uI00ZBSgGYE59UCqqKnDor0NIfZCq8WvO3T+HladX4vfs31Wm0UcNSm0F5QX44doPOJd9DkD1DMCfnfusQcesj0VJi3D32V2UVZRhUdIihcnIZIyMZlE1A1y/GRY87X6+yyvLkfYwDU/LnuoqW1r56uJXnNtNrVmisXBdM8oryw2QE/2hAMUAzKUPCsMwGLBzAIbtGYYe3/TAVxe4f6BqOn3vNPps74MPT36Ivtv74nzOec50jTGK51n5MyxKWqSw7buM7xp0zPqQB0hA9Xlvu7INAPC49DH6bOsDh2gHhO4Irdd6TsQ4cF14tOmDUiwpRs9veiJwSyCe/+p5XHxwkd23O2M3XD5zgcfnHjh486BO8qsNSaWk0d/TFHBdM0xtagUKUAzAXPqgJN9Lxtn7Z9nn847Mq/M103+ezv6/iqnCp2c+5Uyn61E8XFXoBeKCJlWecvKL1bYr2/B7TnUt05n7Z7Dzj52GzJbROHzrMNadX1ev9a8MpaF3xgdvHsQfj/4AUD1/ytLjS9njzv51Np6VP8OTsieY/etsvXzm1TVRiSvFOn+/pubHaz9i2k/T8O0f3+qsuY7rmmFqUytQgKKl/NJ8PCp5hLKKMhy+dRjX8q9pfQyuAMVYa1AqZZV498i7aLGmBUYmjFSoPj5255jWx/vr6V8Kz3/56xfOdJo28TAMA2mVtM4fBa4v+7PyZxoFQromY2T48vyXiPg2Ap8kf6K0Xz6p3/vH31fY/u5v7zZK/pq6q4+uon98f/T8pidO3T2lsG9z2mYM2T0E7/72Lvw2+hlN/wdJlXItgzadZNenrld4fjzrOADg4oOLeFb+jN2eU5Sjl06r6n7fTO2iWlvS7SSM3TsW29K3YfKByTjw5wGdHJerJp5qUMxY3IU4iGJFEMYK4RDtgCG7h8D/f/744doPWh1HV+PXuS7SkioJ/v7nb62PVV+//f0b1l2ovhs9ePMg4i7Gsfu4lv7W1d2DJsfJKshCr229wF/Jx6Bdg1AkKVKZlquauaBcdzUoJ7JOYOjuoZh+cDqelD1Rm/bwrcOI/C0SSXeS8NGpj5T212fWYVOk6jMw5cAUnLp7ChceXMDYH8cqfLdm/DKD/f8/4n/w5YUv9Za/k1kn8eGJD5WCpPpoaBOPi62L0rZiSTHn514fNznqaklMPUB558g7Cs8jf4vUyXG5gj5TK0sKUDQkqZQg8rdIpQWaqpgqTD0wVatj6bMGBQDar2+P3Rm7tT6eKgmZCZjx8wzOyL/2Wigrklew/+dazErbqmpXO1fO7Zr8iK49v5btw5J0JwnfXVXdf4TrDrVSVqmTgKpAXICXdr2EX2/9im+ufIP5v81X2H/r6S28/MPLGJkwEpn5mZh2cJra46kLUPTVbCGuEOPYnWO4U3BH58cuqyjDhyc+xJsH30RmfiYYhsGHJz6Ex+ce6Lu9L+49u8f5Oq6/GVA9+krucdljnLl/RuV7/3rr1wblXZXku8kI2xmGlWdWYkD8gAYvXsn1vdEmkGjh1EJpW2Z+JufvzsBvB2Jx0mKdXuzUHcuYh+/ffXYXWy9vVfjM1fbnkz8Vnt8vvK+T9+a60c3Mz8Tj0sc6OX5TQAGKhu4V3lP5g6Du7uD4neOYlDgJn539jL2T09UEO6ryI2NkdV7kNHXgzwMYv288Nl/ejNHfj8bJrJMK+9WNCODKn7wKslJWiQ2pG7Di1ArkleSx22prSIBSu3lm1q+zVKZV1VGvWFpc5/vUZeuVrQp/32+vfquw/5UfX8H+G/tx8OZBjEwYiUelj9QeT91nxf9//gpV9rogrhAjYHMABn47EJ2+7oTDtw7r9Phzf52LlWdWYuuVrei9rTdO3zuNlWdW4knZE5y9fxYrT6/kfJ2mF1B1F0BVQU5DvXPkHfbzx4DB24febtDxuD6f2nQulcqUA5Fe23ph7N6xStuvP76Oz1M+x6qzq7TLpBriCtOrQckqyIL///zx5s9v4sUtL7KrajcWrutIibQErde1xv4b+xs1L/pCAYqG6tNJ7e9//kbErgjsuroL7x9/H6vPrQag/xoUoDq/d5/d1fqYtb3181sKz7X5oeXKn/zHaN7heZj962xEJUehx5YeqJRV4lGJ8oVZVYCi674h+hyex3Vecvml+bj66Cr7XJMaCnU1KE/KnqitPWMYBodvHcZ3V7/T+Jzj/4jHjSc3AFRf0Bva16VKVoV3j7wL7y+98dr+17AtfRu7r0hShND4UIX031z5hvM4ml7Y1H1W9PV3r/k3Baov+g3BlU9tgqsSaQnndnVl+Mlp5f5P9aXufYw1QFl1dhXbbFwpq9RoEIAuqbpmiCvFeP/Y+5z7apJUSvBe0nvosaUHPjr5Efu7Uiotxbd/fIsDfx7gbKZvTBSgaKiuznQLjy5UuqP5/NznChfpD05+AEC/fVBq0kXb9+MyxerCm09vavxarg+3/G52w6UN7LbsomwcvHmQs3nCycaJ89i6bifX1500ANha2Sptk/8Y1Kc/SV2vOfy36hqOj05+hCG7h+C1xNcQuiNUoyaszWmbFZ5r8xngsvf6Xqy7sA53n91t0LBtTS9s6gJEYxniyhmgaJH3YknDawIbQpMAhWEY7MnYg49OfoSbTxr2GWsMmy8rfi8y8zO1PkZCZgI6rO+APtv6aB3EqqtJvfXPLZVBqdyuq7uwOmU1Uh+m4pPTn2D/jf1gGAYRuyIw+cBkjP5+tFJzdGOjAEVDdVWbx/4eix3pOxS2/fq3cvt22M4wfJ36tdJ2XdegAMDJuyc5txeIC7Dzj51IyU7R+j21wfWjpKqX+Z9P/kRuSa7SdlXlovMARYsf+5rBZIG4ALEp1X97VXcbfCu+0jb5nVd9AtO6mgNV1ToBwMoz/zWXXHhwQWGOFVW4+hI1hK46CWoaoLz1y1sqa5Wa6sRWheWF+Pri10jITICMkemtBqUut57eQuiOULSLa4ftV7bX6xgyRoa159eq3C//O8ZdjMOE/RPwyelP0H1z9yY/Bb4mE+WpuwEoEBdgyoEpuPn0Js5ln9O6Bqau3w5535diSTFnzeybP7+p8Hz2r7Px9z9/K1wXvrr4lUEXdKQARUMF5XX/kWp3GOW66J3IOsH5xdNlHxQ5rruQsooydN3UFVMOTEHvbb0Rnx6v9ftqiqv/RllFmcpZMWvOkCqn6kdY11N/a/NjL+9zVCWrQs+tPbEwaSFe/+l1lU0ffEvVAUp9am7qqkHhGrEBcJdZ2sO0Ot9P19W88j5HDaVN08DCows5t+uz5qy+ZIwMvbf1xpzDczB+33iM/n40Z2CvVQ1KPftSLUxaiOR7ybj1zy28+fObnN/RumxM3Yjvr32vcj/b7FvjAl1WUYYvUpSnxddUlawKpdJSvS4RoEmAomrkIMMw+C7jO4XfQm2nZajrpvbG4xs4kXUCojUiPP/V8xiVMErtNeNJ2RPOa9ORv49olS9dogBFhRNZJzD70GzsSN8BhmHq1fFQm1qRIkkR3jz4JrzWeGFy4mSN7njqClC4ftS2X9mu0It86k9TNc4jF3Xt+1xfzgdFD/DyDy8rbbfgWXB2DlX1I1zfGhRVF1ttfuzlHf4O3TqkMG9LzSHWNVlZKC8aLm92qE8TQ0VVhdrzt7Oy49zOdReuyY+sLmtQdFnzpU2AwlU7BzTNJp70vHRce/zf/EoHbx7kXGKhZnBVVlGGU3dPKQQQOUU5mPHzDEz7aVq9mh/k7y0nY2Sctb91mXN4jtr9qmpV69tEffPJTfht9INjjCNGJozUWy2ZJt8dVVMKlFeWcza7aRNQ1XVTe+PJDXx65lP2WvLTzZ9g+bElhnw3RGVzEtfNz8G/Gn92YTmtA5TTp09j+PDhEIlE4PF4OHDggMJ+hmEQFRUFkUgEOzs7hIaG4to1xcnMJBIJ5s6dC3d3dzg4OGDEiBHIyclp0Ino0h95fyB8Zzg2XNqA1396HTvSd2hdzVVeWa523o3a4v+Ix9YrW/Gg+AG+vfqtUnMRl7p+7LmCnMb8sHHdtUUlR3FOvmbBs+C84KisQalnJ1lV08HXpwZF1TT8tXEFqj239sTNJzfrdQdfIatQOypC1Q8y14VAkx9ZXc67oqshloD2nSu5vi9NsYmH66LGNYxV/rkqEBeg09ed0D++Pzp83YGdxv7lH17G5subFTohN1RdfVkyHmUg7WGaVhdaVX/H+nzHS6QlGJkwku3U/fNfP6uc7LEh5BNA1qV2Hz65Qgl3n8aaQUexpFhtjVVdTTw3ntzgHFl0+O/DmLBvAudruL4Pv9761WCLEGodoJSWlsLf3x/r16/n3L969WqsWbMG69evR2pqKoRCIQYOHIji4v8+2JGRkUhMTERCQgLOnj2LkpISDBs2DFVVhu0xLLf81HKFL8cbB9/AqnPaDbnLKsjS6gtW+0s69/DcOl9TZw2KgecX4Poxqz1TrJwFz0KroZT1vRNX9YNRnxoUro7TXBdzVUFI3MW4et3BiyvEamvYVP3gc30eVAUoV3KvIHhrMLps7KL1xH9lFWVKM5TK1fdOXtX7aIPr/HXdv0YXNO0vIv/sbErbhHuF1XPFFEmK8HXq13hY/FBhvZ3G8NHJj9Dlf10QuCUQs3+drfHrVP0d1X3HZYwMCZkJiLsQp/A9/O7qd0qduG88vqFxXjTBMAzG7Runcl9NqmpQCssLOa8P8rI49NchNI9tDtEaEWYd4p4eoa6g4dbTWyr3yZc9qMnWypYzQCmSFOHMPdVzCemT1gHK4MGDsXLlSowZM0ZpH8MwWLduHZYtW4YxY8bA19cX8fHxKCsrw+7d1Z3UCgsLsXXrVsTGxiI8PBzdunXDrl27kJGRgWPHtJ8aXR+4ok5t77T0MaFVbfWpQdGliqoKteWiTbu3tErKeSHPepaFFmtaYEPqBoXtXOc+6PlBdb6Pqh8MbdYDkf+IPJM8Uz4OR82GqiDk69Sv61WDUlZRpj5AqfzvBz/1QSreP/Y+frz2o9oalGflzzB8z3A4xTghZEcI+u3oh/M555GRn8H5HvIf4j+f/InUB6ns87ySPHT8uiOCvglCp687Kf1IZhVkaXeytd6vJm0DcG1qNPUpPS9dZaAOaBGg/PvZWXJ8icL2nX/sbPTJunKLcxWGJW9K21TnjMly9QlQ3kt6D+P3jcc7R95B8NZgNq18baqadl7dCc8vPCH8Qqh2mvnDtw6jy8YuCPomCJceXlKZ7tLDSypnD6/9fVYZoKioQZGXxYcnP2S/rxsvbcSV3CtKaetq4nlQ/EDt/trsre05f89/n/Y7+nv31+pYuqLTPihZWVnIy8tDREQEu43P5yMkJAQpKdU9g9PS0lBRUaGQRiQSwdfXl01jaDaWNg0+hqoPoC7VFaCIK8VIfZCq8KHj+qHPLc7VuiOkjJGhz/Y+atNoM7RRXCFWGew8LH6IuYfn4kFR9ReOYRilH/Ep/lPwfp+6x/7X/uEuqyjDsN3D8OreVzXO6/A9wxG4OZBzZIj8ByavJA/TfpqGEXtGcI7mkqtP1WlZRZnaNTfkQdJfT/9C8NZgfHbuM4zdOxYbUzcqpZX/oG5O24xf/voFJdISnL53us6LpKRKgi/Pf4mOX3dEj2964LXE1wAAG1I3sM04uSW5SkOU6xsk6GJab3UdFhuD/af24K3godumbmi/vj3W/L6GM522NShcGnsEzJ7MPQrPZYwM9wvva/T5VtnEo+LvUlFVgS9+/68D7Y0nN5B0OwmSSgnnTdHf//xdvYZa6SPM/GUmW8sprhAjuzAblbJKlFeWY+L+icjIz8DFBxfxxk9vqHz/2usa1VT7N09dDQrXWkrysriSpxiQfJ7yuVLaupp4tO03aWdlp/Qb3L15d/T06qlRU7A+KPfea4C8vOre+Z6engrbPT09ce/ePTaNjY0NXFxclNLIX1+bRCKBRPLfl7GoSL93QtaW1vV+LcMw4PF4Om1ekTEyVMmqlPKlSTNHj296oKN7R6RMS8Fzts9xphGtEaGnV08cmXgEAluBRnn65a9fVFYhyxgZLHgWWl2MyirK1NYmyBgZruRdgYeDB1754RX8/NfPCvsteBZwsHao831qN/F8fu5zHLp1SON8AtUXXlWdLuU1MYuSFmHX1V11HktdNawqablpan985D9yH5z4QKEJg+uHVR7MaDspl7hCjNUpq9nnuzN2Y0HwAqXjfPH7F/g84r8f1/oGKJIqidJwbW0XRlP13pIqCedcNbpWu5Yu+kw03u35rtKaOtrUoKi6CahrNuL6UtVsnZCZoLTtceljlX2+aqqrBuXMvTP4X9r/4GjtiAsPLnA2T7z03Ut1vg9QXS63nt6CtaU1Bu0ahDsFdxDUIgiLei1SGKmZkZ+BEmkJnPjK8zCp6/9VLC2Gh4MH+1zVdeBZ+TOVqxFz3ajVni4fqN/NjTpcNSiN8b1QRy9hUe0vnPyirY66NDExMRAIBOyjZcuWOssrl4bUoMj/wLpqXvnfpf/BMdoRojUirPl9DR6XPmbvnDSdQ+PGkxuYdWgWfvnrF5Vt7udzzms1aVbtO6aapFVSVFRVaN3xtK7+GOIKMfZe36sUnADVAYq9tX2d71Pzws4wDKKSozTOoybkP16//f2bRulrLySmqVd+eEV1Hv69EGrSOVCeVtvPa1lFmdLEeurWOpKrb4DC9aOtqyYebfNUJCnC2ftnG9yM8lT8lPM7os3fQlVTRGMuGFolq1K64weqa3HULYUhV1pRyr2wKBjkFueif3x/7M7Yjc2XN3MGJ9qSVEnw1YWv2Gb4Cw8ucHYk5ppaYnPaZvx4/UeVx679WVLVdFwoKeQMdEqlpZwDMmo2Cf4j/gev/PAKos9Gq8xHffB4PKXPo0kFKEKhEACUakLy8/PZWhWhUAipVIqCggKVaWpbsmQJCgsL2Ud2drYus63E2qL+NSjyD6gulr1+Vv4M7/72LsSVYjwpe4IFRxeg2RfN0PHrjkjPS9dobha5PZl7MHzPcLXrRWjasa1KVqW2fVlVVas6uzN2Y9+NfWrTiCvFKtcY4oEHB5u6a1BqXtTkPf11SX43qKozrq6oO748D5qMvpH/SLrZuWn1/lyfvQsPLtT5uvrOx8EVvGr7HVPVn0abAOVh8UN02dgFfbf3RcevOza40y9X7YE2AUrtKfXldHEh11R+aT7nZy2/NF+jGpTM/EzOdDJGhjW/r9F5R+ZSaanSlABci0bWDhTkv8fq1K7RUlU7VFheyLmvrKKMsyxKK0rZqQnWX1xf529lfXA1s5tUgOLt7Q2hUIikpCR2m1QqRXJyMnr16gUACAgIgLW1tUKa3NxcZGZmsmlq4/P5cHZ2Vnjoy4WcC7hdcLver5f/2OmiBmXQrkGcd45Zz7KwKGlRg4/P5fvM7yH8QohWa1uprAWQB0yqqKt6VkWTYEtdPxVNm3hq/ijsu66HL3mlWC/L1WuVh3+DDo0ClH/v8Fo/11qr9+C6y+OaldaSZ6nwvCFNPEB1s4G8j4u237EFRxdwbtcmT19f/JodMfNU/FRh9e764LqL1ua8VK1erW51XV3LLuK+YcwvzcdTcd01KAAwft94pW3lleUKfU10RVUH19pqBwrH7xyvs99T7QBcVXNQoUS7AAX4b4j+8lPL1eahvsory5tcgKJ1H5SSkhL8/fd/1YdZWVlIT0+Hq6srWrVqhcjISERHR8PHxwc+Pj6Ijo6Gvb09JkyoHnctEAgwbdo0LFiwAG5ubnB1dcXChQvh5+eH8PBw3Z1ZPRSWFyotVKYttgZFB31Q1A0T1HbWQU3N+GUG28FXVW1F2sM0tVW3kkqJzlfUBdR3itS0iafmXff+P3W/4qe4Qmzwxc/YtU00GOYu/wHVdrizJnfGQPUw3lJpKVu7Vd8AJe5CHPZk7mFrjub2mKuTWkqg7nW2aqpdrb73+l72/7/89Qs+OvmRyr5eXGp/Vh4UPdBo+QG5vFLufnu6WCiUS+3PibhCrLTCuVx+mWY1KABwPOu40jZ9jYT86uJXGqWrnXdNalw1buIpL1QYbSe38dJGvBXwFscr9F8rK65sejUoWgcoly5dQv/+/w05mj+/ejGhKVOmYMeOHVi8eDHEYjFmzZqFgoICBAUF4ejRo3By+q+z0dq1a2FlZYWxY8dCLBYjLCwMO3bsgKWlpdL7NaZtV7Y1eOImtgalQr9DfPWl5ugjVcPU6griyivL9fJlUjcUmMfjwc6aewbVmuQXtTsFd/Ryl1lWUWbw+WduF9zWeFRSffugjPp+lMZpH5U+QlubtgDq38RT+6ISdzEOfs386nWs2nRxMX9W/gzj943XuhzFlWIwDIMiSREO/HkAr//0ulbzJ527r3kwows1v4O3/7mN0PhQ5BRxT7K5I30H2gjaNE7G9KB2gJL6MLXO16y/uB7jfKvnSLlfeF9l7ZKqGpTDfx9WOQJL3yOzOJt4LI0sQAkNVb8CKo/HQ1RUFKKiolSmsbW1RVxcHOLiuKcGNxRd/FCtPb8W/kJ/g1+kDElSJdF4DgRtqKu1seBZsLUo6mowSqWlKJIUIeLbCJVpGmLU96Pwy3jdz1ypLU2rseUXHF3VRnB5VPIIbV2qAxRdzkWiqk+JtnQxedxPf/5Ur2bdu8/uYlLiJJV9SerSkObo+vhH/A87Sm/V2VUqgxM5XXdCb0xv/fIWBvsMhpezF4DqOYXqci77HM7cO4ODNw+qbZ4qlBSqvEak5XKvj6XvuW2qmCqlpnlD16DQWjw1cK2Zoq2f//oZXf/XVS8XaGNRXlmuNP+FLtSeIbIm+ZwCdfVDKZIUIWRHiF5/2IftGaa3Y+uavIlHn5P61bzzayqTpdVUc92b+pL3S9HWe8feq3dwYgiHbh2C5xeeOPL3EXxz5RtDZ0fvlp1YBqC6ZlTV1AK1fXjywzr7zjwrf6Z1U7C+m3gA5b6Ahg5QdDoPirFryPwnNWUXZaus2jMH7xx+h3NGx4bimgtATj6RUF39ULjaus2ZuFKMKlmVXtekqTknhzEHKOpqjjXta1Gbus90U/Wk7AkGfzfY0NloFDv/2ImXO76MbsJuGr8m+V5ynWku5FzQavZqwDwDFKpBqaEhw4vJf/QRnADqq7PlAYomQ43Jf8QVYr027wBgFzyra2kEQ8kpyqmzoyzDMBi7d6zK/Y3d1EIaz8iEkRot3qoNbYMToLomUt8jBGsPbqg9OWJjowClhvqukEsMTz7JnyZDjcl/MvIz9L5uVObj6j4eqtrWmwJ5LcrTsqd4addLcIpxwuTEyWxAlZKdojBipyYZI6vXjMD6oMlINqK9j059ZOgs4HHpY7V9G9dErMHpqacb9B6Xcy8rPKcalCbE0MNDSf3VtwZF1QKDK/uvBLOcgewjGe68o/+FHw2lrKIM3TZpXn1dH2kP01BeWY7grcF6fZ+G6L2tN6b9NA2DvxuM327/hhJpCb69+i3cVrvh3rN7CtP611YkKWqUxUE10dG9o6GzgK+HfG3oLJikx2WP1Y6Cs7a05pyavyEoQGlC9Dny5sCrB/R27JDWIejfxjCrTTYVmvZBqUnoKMS2kcpTXAP/VW3yeDx4u3jjw34fNjyTZirrWRYO3zrMuW9NBPeCeYawLX2b0lDSsooyBH0TpLbT+19P/6pzZdnG0t69vUHf35JniZmBMxE9QLfTsJPqGhR1E2DaWNrAma/bSUwpQGlC9NkW30rQCi+4vlBnOm1XjXSyccLxycdxdNJR/Dz+Z52sxGyMNB3FU9Oel/dAwOdeHJFvqdj22tmjc/0zZ8Re6/IapB9I4enAvQyFpuSjIWqL7BmJvf+3FzFhMU32zvtR6SOkZKteab0x172R692yN+f2Dm4dGjknimytbGHBs0CAKMCg+WhMFjwL7P2/vSr/JrpSWlGK1edU1+RZW1jDyYZqUEyWPgMUBxsHONo41pnueZfntTru0HZDYWlhCSsLKwxrNwyf9NduVVpToW0Tzwd9P0Bom1CVk7vV7hzm6diwC7SxYhgG1pbWGOA9QOPXlC4txYuiFxW2qZqFk8fj4eVOL+P9Pu+zc6XUl7+nf4NeX18Nne6+LrWbbYa3Gw43e+W1k/iWfK2XLNA1+fdGVeBvKib6TcTTxU+xa/QuXHzzIl7u9LJGN6ANxbWooVx9alDkc7yoQgFKE6LPPiiONo7oLuxeZ7o2z7XR6ritBYo/SCPbj1Ro5vh84Ofo4N5Bo+BIEy2cWujkOLrGNvFYadbE83Knl9nXcdW6eNh7KDxvaA2CsZIv1Kbp8OBXOr0Ce2t7vNHtjTrTBrUIUngurwWrr9OvN6yDYH3VXGlW17yf88aGoRvYsrHkWWJ5yHLOxR1d7FzQzKGZ3vKiCXnNo8DWOAOUVztrNgOzq50rXO1cMbHLRLa2qK6Lvb5ZW1qDb8XXeDTqeN/xddY4U4DShNS3D4om7a0O1g5YPXA1+rbqqzadtgHKK51eUXje3r09UqenIjYiFmdfP4uFvRbixuwbKHy/EFO7TtXq2LW9KHpRowuPIbCjeDSsQfF+zpv9v6WF8hILz7sq1mQ19RoUfQWO8gUHNZlmOzYiFjtH7QQAvBXwFv6v0/+pTR/ZM1Lhed/WfRs0CsvRxhHjfZUXnTNGbZ5rg/Zu7bFt5DaEtgnFuTfO4bPwz3Bx+kUEiAI4A5Q2z7VRG6BEPK+72ZN7t+zN+V7GXoOS8EqCRhdlrvJv6dxSH1nSmDww0aSj7If9PsSmYZvqXB6EApQmpL5NPK91eQ3HJ6ufAMzBxgFu9m5InpqMk1NOYkUod7Vw7RoRdV7v+joCRYFK2zt5dML84Pno3eq/NlELnkWD53nJK8mDi62L1q9TNfStdj+PhmCbeDS8wNW8w+OqHagZwADgPO8eLXpgfs/52mRTb7aN3IZh7Yahe/O6a+m0USWrrkGpOdkal7e6v4X5wfPZHzwLngXiBsep/Ht8Fv4Zu2aJnL21PX74vx9UnoPQUQgLngUW91rMud+CZ4H1Q9ZjQfACTPafXOfNQGePzujp1VNtGkPwsPdA1rws/DnnT4S2CQUABLcMxuLei9my4Wri6ezRWWWAsqTPEnw35jud5O//Ov0fzr5xFo8WPlJaGHFsp+q5YnTdWbMx2FlVf3Y1qW12tXNV2qbrGhRnvrNW32d5YMJV9i93fBmZb2fiyowrYJYz+Lj/x3DiO+HGY/ULIFKA0oTUtwaFb8XHAO8Baj+g8mn0eTweQtuE4qOQjzhHnAgdhRq9Z2ePzlp3KmxogJJdlA0XO+0ClA/6fgAfNx/OfYmvJqJHix7wbebboHwBYPsv6Gqittp3IfIampoYhmkyQ9M7uHfAz+N/RtpbaXg78G2dHVfexFPX55LrTszT0RNjOo7hTK/qbn6IzxCkvZXG2Z8kd0Euqj6qwmcDP1OZD1c7V3wR8QXiR8Ur9YOpLdgrGL9P+x2lS0u1rrnUJ01q67ju4Dt5dFJqmgSAmQEzER0WDXd7d53kr2ZQ8vnAz9n/21vbY37wfPb/xkYedGhyk8MVoLQU6LYGZXr36ejk0Unj9PKAnKujbGePzujcrDO6CrsqbJdUqV/FnAKUJqS+NSjykTPv9HiHc3+vlr04t3P1a9B0qfbvX/leo9V7a9LFVP7aLCUPVM9MqKrWZYD3AFx48wIy3s5ocNv58HbDAWj2w1ifWiAufCt+vWaE1Iead31cP571NdFvIoDqQFMd+d1nbcPaca9LVLuGqra6yrWVoJXa/UDdP67y5gh7a/sm1TSkSZMxVw1KJ49OnDN/ypvpdKXmb8Cb3d/ET+N+wqcDPsUfM/9ggyuugF5XRE4iPJz/UOfHlfc/0eSirIsalPd6v4fiJcWQfCDhDJDD24ZD5CjS6Fj7x+5n//ZcNSidm3GPQqyrz40ua7nrgwKUGupdg/LvH3FR70U4+/pZ7Bu7D7ERsWjn1g7BXsHYNGwT5+u4Lsoudi4a9QbXNjgBgOaOzbV+TU0tnVtqfXF/6YWXVE6XXHO7JU+5H4gqtfPg6eDJ/mBrcvdT3zvJN7u9qfB8Wd9lGN1htMI2XSw4WR81AxRtg0hV/D39MarDKADAYJ/BWBC8AN7PeXNWO3P14wGqJ8Kr/SMX5h1WZyfKumqmpnefrvC8vZvy/B91TdNdc0j+2M6K09h3cDfMcN1xvuMwxGdInem41gWSj/YROSle1Mb76Tb4qv39G9F+BJb2XVqvUSyadkqt+d4//t+P8HT0VAgINK2xmd59Oma/OFtpu4O1A97v877G+eAKKFxsXZTKvrbRHUbjeZfnsbL/SkSHRcPRxhE2ljacfXYCRYFo4Vx337Jjk45hdMf/foe4psNXNU3C611fV3tsqkFpQrhqUNYNWoeXO76s9nU1f+h6t+qNMR3HYH7wfNyccxMp01JUNmFwVeW62LpgSZ8lbK99v2Z+GNl+pFK6+lShTg+Y3qB5Upb2XarV+/q4+mjcMY/rAqeq09nCXgsVAoGEVxLY/9f1AwEoByi1f2wGth3I+br3+7yPLp5dAACT/ScjvG04hrYbyjZHWPAssG2E6mGA+lTz76rJejdvdFXd2XlZ32VImpSEC29eYI9rZWGFLyK+wJ15d/DL+F+UXqPqLl1gK8Bn4Z+xn+fh7Ybj+1e+rzN/dQUokT0jFWogZ704SylNXXd/NRdG6yrsir3/txejOoxCTFgMVvZfWWcedenS9EuQfCDBnpf3qAz2agryUhwB9Zztc2wTQ2xELPv96NOqD9uPRVc8HJSbkeprVIdRWgUpf875E71a9oIFzwJrB62Fo40j+JZ8fDHwC84pGmrOK2VlYYXosGjEDY7Dd2O+w9SuU/Fyx5fx6YBPcfXtq+x51bXkSZvn2nAGsDweD6vCVqn8jXWzc8P+V/fj73f+xrJ+yxTyxjUSzN3evc7fs0W9FiGsbZjCNq6FalU1sw96YRD+mPmHyuMbei0eWs34X9IqqdKPbFRIFN4JegfD2w/HP+J/kF2UzTkpkyY/KFy47vafs30Ob3R7A12FXZFdmI1BLwzCa/tfU0qnqkpdHVc7V+wbuw/LTixjl3hv4dQCc3rMwZLjS9S+9oO+H2B69+m49U/da47MCpyFnl49MbLDSI2blbhqUK7MuAL3z5VrO8b5jkOYdxiS7iShf5v+Cp2BQ9qEIFAUiEsPLwEAIoMi8XvO77jw4MJ/+at1MVsRugJTDkxhn68ZxD276fOuzyN9RjoAxSrs36f9jpN3T8LL2QtdPLtg5ZmVeh16Wpe6gkihoxBbR26tniH3pPIMuVO7TlV7N8zViVDemZbLvJ7z8H+d/w/SKqnGfT1CWocg8c9EtXn4Y+Yf+P7a93je5XkMbTdUKU1dP67X8hVXMX6508vs8PNTd09plM8WTi3woPiBRmnVcbVz1ermwcvZCzMCZmBT2iZY8iyxKmwVe8Eb5zsOgaJA5BbnIrhlsNaTP6pja2Wrsl9RffAt+Uh4JQEyRoYfr/+oNu3bgW8r1Dq/0ukVjOowCjJGBhtLG/i4+WDgt//dXGwYsgF21nZ4+9DbkFRK8EHfD9ibkwl+EzDBbwLn+9S1IN/wdsNVNmFN8p+El154CfOPzseuq7sU9qmr9X6/z/tYfmo5+1xe46FuZJCjjSPbBFtTTlGO0jZ1n60unl2Q/W42wneG4+bTmwr7Gjr0v6EoQPkX1x3btO7TwOPx0NalLU5MOQEAmJw4Gd9e/VYn78n1oZF3Qu3evLvaHtz1aeIBqvsEDGs3DJWySuQU5cDD3gN/Pf2rzgDlkwHVE8C1d2uP9m7t2Q+yl7MXYsJi8Nvt3/Cs/BnCvcMxp8ccrYM2rvSqzrG1oDXaurRVuosEqsv09NTTOJ9zHm2eawNvF28k3kjEq3tfRYWsAl2FXZXu2CZ1mQRLniUuPriIVzq9orbTLtcPk521nUK1/LpB6zDmhzEoryxHoCgQJdIS/PnkTwDVzUTJ95I1CvTqa2znsVh4dKHKO0H5kORxvuOUApRmDs3qnCyQKwCSd6ZVRZOarZqWhyzHgT8PsOewdcRWpTSejp54J4i73xdQdw2Kuk60mvbjuTPvDvgrG36XWZ9+QxuHbkRkz0jYWdkpTdD2gusLGje5fNL/E/Rr3Q8hO0LYbaM6jMLzLs8j9vdYhbTrB6/XaR8n+Z39RyEf4cz9M8gryeNMFxsRi7k95iptr1mTGuYdhv8N/R8S/0xEsFcwpgdMh5WFFUZ3GI1KWSVnvx0udQUoddX4eDh4oJ1rO6Xt6m4qx3Yei9XnVqO0ohQ88LBx6EYAQIAoAK0FrXGv8B6A6o6w8aPicfb+WfRq2UtpOgSg+m934M8D7HNNar29nL1wbdY1eH/pzdbAtBa01qivlz5RgPIvrv4nXH9YXXWwBLhH1Wg6PK+hI3KsLKzYu9m62jlrDsXk8Xg4MO4APjz5IXjg4dMBn8LHzQevdVGu5dEG110eV/vnpC6T6gx+7Kzt0N/7v7WJRnccjeuzr+N+4X30adVHqVaHx+NhYpeJmNhF+W6kPgb7DMbNOTfxoOgBAkQBEFeIsfXKVjjznTG161ScvX8WYTvD9LZ0upezFzYM3YDoM9Gc1b3yi/4Lri+wd+Fy4W3D6+zgyFX+uj4Xf6E/kiYlYd+NfXhR9GK95vCpq/1c3TE1/Z7bWNrgo34f4ePTHwOovnh9f63uJqyaLHgW9Vrkjcfjad1XpnfL3jiXfY59/lqX1/BBv+oO0F8M/AKrU1ajtaA1VoWtQnOn5qioqsDNpzfxVsBbOqk5qfl5C20Tyt4M+DbzxZ+z/0Tin4l4/SfFfhFrB61VmjOHC4/Hw4zAGZgROENhu7aTxnH17+nRogf+/udvvNvzXYUaW1W4RhOqu6ns4N4Bl2dcxqm7p9DTqyfblGxlYYXTr5/G2t/XQmArwOLei2FvbQ9vF9WdzOf2mKsQoHw7WrMbaksLS+waswvv/vYueOBh3Uvr9NrZWRMUoPyLq/8JVxPM6I6j8dXFr9jnDZmQiOsDy3Wh5roT1uUHR12nURtLG7zX+z2FbR3cO+DH/1NfHastrvO24FmgX+t+OH2veh4VB2sHrApfVa/ja3NHqQutBK3Yuw8bSxt2+CVQ/cOc8XYGLj28hM/OfYbrj6/r/P1nBs7EzMCZqKiqgM1KxZq6mhfutYPW4knZE+y7sQ8d3DuonJ+nLuqaeOorrG2YUvu6Nri+N+3d2qNb8274v07/hxdbqK5B0WY4/Yr+KzDEZwjKKsoQ0iZEbYDiZOOktCKtjJHptBlGndiIWPSP7w9xpRjP2T6H5SH/NSss6LUAC3otUEj/5eAvdfr+G4ZuwADvASiVlip13hXYChDeNlzpNY29vhhXsH3hzQtgGEbj312uZtC6mjfbubVDOzflmpdWglZY+9Jajd4XqB4duW/sPhy+dRghbUKUOvKr0691P6S9laZxen0zaCfZDRs2wNvbG7a2tggICMCZM2cMlpfaNSiWPEvOL0ZI6xD2S8QDr94XTKD6bqKm2lN/NxYLnoVCE4WAL0Duglycn3Yet+beYkdyNETtatGQ1iEKz1WN4tkwZAMGth2Ivq364qdxP2ndVNBUdfLohMn+k5E0KQmvdXkNQ32G4uSUkwrnJ6/mrQtXJ2o5a0trTOoySWFbzSG1dtZ22Dt2L8qWliHz7UyNg7iA5oqLwU0PmK4ipeFw1TImT03Gnpf31FkboO2MtkFeQejv3b/OQGPtIM0vNPoQ5BWE9Jnp2PPyHlydeVWvQfu0btMUnoe2CYUFzwJjO4/F691e56zh4pp6obGn71dVG6jNTSHX52dAG83Xs2qoMR3HYMuILXity2sGrwVpCIMFKN9//z0iIyOxbNkyXLlyBX379sXgwYNx//59g+Sndg2Kg40D5x+Wx+PhyMQjOD75OK6+fRUzA2fW+z07N+uMmQHVrxfwBfi4/8ec6Rqjo9LWEVsx2X8yhvgMwU/jfoLQUYggryCdtUEuD1nOtsFaW1jj0wGfKuxXNclR52adcXTSUZx+/XSD7qabKpGTCN+O/ha/TPgFoW1C8cfMP7Bp2CYcm3QMMwNnKg0N3zBkA2YF/tfJV8AXYGGvhWrfY0XoCrbfSTdhN86OdXbWdlr1G4oJi2GHM7/e9XW2Srop6dtacSbZwS8M1njJAh6PpzCay9bKFicmn1AIpOMGx3G+NtgrmHN7O7d2GO83HhuGbFDYrsmwYl1q59YO43zH6XxisdqW9FnC1jDbWtlqNL+LtaW1ws2LgC9o9PLRxbIWXPP4mOLvl77xGK4Gt0YQFBSE7t27Y+PG/+4SO3bsiFGjRiEmJkbta4uKiiAQCFBYWAhnZ91MqXz98XVEn4lGaUUpSqWlsLO2w0/jftLJsevyuPQx7KztVE6x/OGJD7HyjOKwR2a5Qf5sDXLr6S2cunsKQV5BShe0K7lX0H3zf52CF/VahNUDVS8tbi5+vvkzxu4di/LKcvRu2Runpp6ClYUVKmWVyHiUAS9nL42GfUoqJcguykZrQWudTNgHAMWSYpRWlGo8+7EhbE7bjHXn16GloCU2Dduk1Yyx1x9fx7wj81AkKcLSPksxssNIpD5Ixe6M3fAX+mOK/xTOm5hLDy/hxS3/NR8t6rUIA7wHoG+rvnCwcUBFVQXG/DAGv/z1C1ztXJH4aiL6te6ni9NtcnKKcnDm3hl0b94d7d2V56rhcvuf25h/dD6elT9DVEiUQn+yxnAi6wTCdv4XTCwIXoAvIr7Q6hipD1LR45seCttkH8mMujZDV7S5fhskQJFKpbC3t8ePP/6I0aP/ax+bN28e0tPTkZycrJBeIpFAIvlvSt6ioiK0bNlSpwFKU/ak7AlEsSJUyCoA1O8L09QxDIMNqRuwLX0bOnt0xpcvfan1tPqm6n7hfeQW5yJAFGCwieCIdn6++TP23diHHi164O3At5UuTDJGhuzCbAhsBTqbWI/ohoyRYdnxZdiVsQv+nv7YOmKr1rUqMkaGAfEDkHyv+lq2ZfgWvNn9zTpeZR6afIDy8OFDtGjRAufOnUOvXv9NAx8dHY34+HjcvKk4FjsqKgorVih33jOXAAUALj64iA2pG9DWpS3e6/2ewSfQIYQQopq0Sopz98/B09FTqzV1TJ02AYpBb8dq31Wo6iW9ZMkSzJ//3ygIeQ2KOenRogd6tOhRd0JCCCEGZ2Np0+jNU6bGIAGKu7s7LC0tkZenOClPfn4+PD2Vq9L4fD74fKoxIIQQQsyFQUbx2NjYICAgAElJSQrbk5KSFJp8CCGEEGKeDNbEM3/+fEyaNAmBgYEIDg7G5s2bcf/+fcycWf9hu4QQQggxDQYLUF599VU8ffoUH3/8MXJzc+Hr64tff/0VrVu3rvO18n69RUVF+s4mIYQQQnREft3WZHyOweZBaYicnByz6yRLCCGEmIrs7Gx4eXmpTWOUAYpMJsPDhw/h5OSk84lv5COEsrOzzWYIsyFQOTceKuvGQeXcOKicG48+ypphGBQXF0MkEsHCQn03WKOc9cnCwqLOyKuhnJ2d6cPfCKicGw+VdeOgcm4cVM6NR9dlLRBotsiuQRcLJIQQQgjhQgEKIYQQQpocClBq4fP5WL58OU0Mp2dUzo2HyrpxUDk3DirnxmPosjbKTrKEEEIIMW1Ug0IIIYSQJocCFEIIIYQ0ORSgEEIIIaTJoQCFEEIIIU0OBSg1bNiwAd7e3rC1tUVAQADOnDlj6CwZndOnT2P48OEQiUTg8Xg4cOCAwn6GYRAVFQWRSAQ7OzuEhobi2rVrCmkkEgnmzp0Ld3d3ODg4YMSIEcjJyWnEs2jaYmJi8OKLL8LJyQnNmjXDqFGjcPPmTYU0VM66sXHjRnTp0oWdqCo4OBiHDx9m91M560dMTAx4PB4iIyPZbVTWDRcVFQUej6fwEAqF7P4mV8YMYRiGYRISEhhra2tmy5YtzPXr15l58+YxDg4OzL179wydNaPy66+/MsuWLWP27dvHAGASExMV9q9atYpxcnJi9u3bx2RkZDCvvvoq07x5c6aoqIhNM3PmTKZFixZMUlISc/nyZaZ///6Mv78/U1lZ2chn0zQNGjSI2b59O5OZmcmkp6czQ4cOZVq1asWUlJSwaaicdePgwYPMoUOHmJs3bzI3b95kli5dylhbWzOZmZkMw1A568PFixeZNm3aMF26dGHmzZvHbqeybrjly5cznTt3ZnJzc9lHfn4+u7+plTEFKP/q0aMHM3PmTIVtHTp0YN5//30D5cj41Q5QZDIZIxQKmVWrVrHbysvLGYFAwPzvf/9jGIZhnj17xlhbWzMJCQlsmgcPHjAWFhbMkSNHGi3vxiQ/P58BwCQnJzMMQ+Wsby4uLsw333xD5awHxcXFjI+PD5OUlMSEhISwAQqVtW4sX76c8ff359zXFMuYmngASKVSpKWlISIiQmF7REQEUlJSDJQr05OVlYW8vDyFcubz+QgJCWHLOS0tDRUVFQppRCIRfH196W+hQmFhIQDA1dUVAJWzvlRVVSEhIQGlpaUIDg6mctaD2bNnY+jQoQgPD1fYTmWtO7du3YJIJIK3tzfGjRuHO3fuAGiaZWyUiwXq2pMnT1BVVQVPT0+F7Z6ensjLyzNQrkyPvCy5yvnevXtsGhsbG7i4uCilob+FMoZhMH/+fPTp0we+vr4AqJx1LSMjA8HBwSgvL4ejoyMSExPRqVMn9geZylk3EhIScPnyZaSmpirto8+0bgQFBWHnzp1o164dHj16hJUrV6JXr164du1akyxjClBq4PF4Cs8ZhlHaRhquPuVMfwtuc+bMwdWrV3H27FmlfVTOutG+fXukp6fj2bNn2LdvH6ZMmYLk5GR2P5Vzw2VnZ2PevHk4evQobG1tVaajsm6YwYMHs//38/NDcHAwnn/+ecTHx6Nnz54AmlYZUxMPAHd3d1haWipFgPn5+UrRJKk/eW9xdeUsFAohlUpRUFCgMg2pNnfuXBw8eBAnT56El5cXu53KWbdsbGzwwgsvIDAwEDExMfD398eXX35J5axDaWlpyM/PR0BAAKysrGBlZYXk5GR89dVXsLKyYsuKylq3HBwc4Ofnh1u3bjXJzzMFKKj+AQoICEBSUpLC9qSkJPTq1ctAuTI93t7eEAqFCuUslUqRnJzMlnNAQACsra0V0uTm5iIzM5P+Fv9iGAZz5szB/v37ceLECXh7eyvsp3LWL4ZhIJFIqJx1KCwsDBkZGUhPT2cfgYGBmDhxItLT09G2bVsqaz2QSCS4ceMGmjdv3jQ/zzrvdmuk5MOMt27dyly/fp2JjIxkHBwcmLt37xo6a0aluLiYuXLlCnPlyhUGALNmzRrmypUr7HDtVatWMQKBgNm/fz+TkZHBjB8/nnMYm5eXF3Ps2DHm8uXLzIABA2ioYA1vv/02IxAImFOnTikMFywrK2PTUDnrxpIlS5jTp08zWVlZzNWrV5mlS5cyFhYWzNGjRxmGoXLWp5qjeBiGyloXFixYwJw6dYq5c+cOc/78eWbYsGGMk5MTe51ramVMAUoNX3/9NdO6dWvGxsaG6d69Oztsk2ju5MmTDAClx5QpUxiGqR7Ktnz5ckYoFDJ8Pp/p168fk5GRoXAMsVjMzJkzh3F1dWXs7OyYYcOGMffv3zfA2TRNXOULgNm+fTubhspZN9544w32N8HDw4MJCwtjgxOGoXLWp9oBCpV1w8nnNbG2tmZEIhEzZswY5tq1a+z+plbGPIZhGN3XyxBCCCGE1B/1QSGEEEJIk0MBCiGEEEKaHApQCCGEENLkUIBCCCGEkCaHAhRCCCGENDkUoBBCCCGkyaEAhRBCCCFNDgUohBBCCGlyKEAhhBBCSJNDAQohhBBCmhwKUAghhBDS5FCAQgghhJAm5/8BJtJ0ZSRK6ZUAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.subplot(2,1,1)\n", "plt.plot(L,spectre_moit,linewidth = 3,label='spectre de f'); # plot du spectre d'amplitude de f sur la première moitié des fréquences\n", "plt.legend();\n", "plt.subplot(2,1,2)\n", "plt.plot(L,spectre_func_moit,'-g',linewidth = 3,label='spectre de funclean');\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "dd728c58-bffa-49c3-9e64-a041ab5ccb0d", "metadata": {}, "source": [ "### Q11 Débruitage de $funclean$\n", "Afin de débruiter le signal $funclean$, on va mettre à $0$ les fréquences d'amplitude dont le module est\n", "inférieur à $r > 0$, un paramètre. En vous aidant du spectre d’amplitude de $funcleanhat$ proposer une\n", "valeur de $r$ et effectuez le débruitage. " ] }, { "cell_type": "code", "execution_count": 51, "id": "3afd8055-e5fb-46c6-a0e6-2c653095d2e5", "metadata": {}, "outputs": [], "source": [ "r=250\n", "spectre_func_debruit=funclenahat*(np.abs(funclenahat) >r)" ] }, { "cell_type": "code", "execution_count": 54, "id": "e9787cfb-1b5b-48ea-ae07-bb57d71c54e9", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n=np.arange(N)\n", "plt.subplot(2,1,1)\n", "plt.plot(n[0:500],spectre[0:500],linewidth = 3,label='spectre de f'); # plot du spectre d'amplitude de f sur la première moitié des fréquences\n", "plt.subplot(2,1,2)\n", "plt.plot(n[0:500],np.abs(spectre_func_debruit)[0:500],'-g',linewidth = 3,label='spectre de funclean tronqué');\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "80635cbd-e1a7-457a-b667-5cbb14272ad5", "metadata": {}, "source": [ "**Remarque sur le débruitage de $funclean$ proposer à la question Q11** \n", "\n", "L'opération décrite à la question précédente revient à appliquer un filtre au vecteur $funcleanhat$. Notons $H=(H_n)_n$ les composantes de ce filtre. Dans le domaine fréquentiel la définition de $H=(H_n)$ est la suivante\n", "\\begin{align*}\n", "H_n = \\left\\{\n", " \\begin{array}{ll}\n", " 1 & \\mbox{si } |funcleanhat| \\geq r,\\\\\n", " 0 & \\mbox{sinon.}\n", " \\end{array}\n", "\\right.\n", "\\end{align*}\n", "où $r$ désigne la valeur du paramètre choisie. \n", "\n", "On considère alors le vecteur $fcleanhat= (fcleanhat_n)$ avec\n", "\\begin{align*}\n", "fcleanhat = funcleanhat \\otimes H,\n", "\\end{align*}\n", "où $\\otimes$ désigne le produit de Hadamard." ] }, { "cell_type": "markdown", "id": "670dc7a3-a2cf-4414-9ca0-c92ec6425f7d", "metadata": {}, "source": [ "### Q12 Retour au domaine temporel. \n", "\n", "Utiliser l'inverse de la TFD \"np.fft.ifft\" de la librairie \"numpy\" pour revenir dans le domaine temporel et déterminer \n", "$fclean$.\n", "\n", "Puis sur une même fenêtre graphique, tracer $f$ et $fclean$. \n", "Le filtrage précédent a-t-il permis de débruiter $funclean$ ? Si tel n'est pas le cas, considérer une nouvelle valeur de $r$.\n" ] }, { "cell_type": "code", "execution_count": 56, "id": "338dae3d-8a3e-404d-934f-8a85f6ab4862", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "\n", "fclean=np.fft.ifft(spectre_func_debruit)\n", "\n", "\n", "plt.plot(t[0:200],y[0:200],'-b',label='signal f'); # à la même échelle sur l'axe des ordonnées\n", "\n", "plt.plot(t[0:200],fclean[0:200],'-g',label='signal débruité');\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "6e188dbd-5a07-40b4-9904-bc20b5b03396", "metadata": {}, "source": [ "**Remarque** Il est important de comprendre que si la définition du filtre $H$ est naturelle (ou en tout cas intuitive) dans le domaine fréquentiel, sa définition dans le domaine temporel est beaucoup moins aisée. En particulier, noter qu'un filtre passe-bas, passe-haut ou passe bande est souvent (toujours) défini dans le domaine fréquentiel." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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 }