Image spectrale d'un signal.ipynb

{"cells":[{"cell_type":"markdown","metadata":{},"source":["---\n","\n","<H1> <center>Filtrage de Fourier</center></H1>\n","\n","---"]},{"cell_type":"markdown","metadata":{"toc":true},"source":["<h1>Table des matières<span class=\"tocSkip\"></span></h1>\n","<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Documentation\" data-toc-modified-id=\"Documentation-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Documentation</a></span><ul class=\"toc-item\"><li><span><a href=\"#scipy.fft.fft-:\" data-toc-modified-id=\"scipy.fft.fft-:-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>scipy.fft.fft :</a></span></li><li><span><a href=\"#scipy.fft.rfft-:\" data-toc-modified-id=\"scipy.fft.rfft-:-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>scipy.fft.rfft :</a></span></li><li><span><a href=\"#Conséquences\" data-toc-modified-id=\"Conséquences-1.3\"><span class=\"toc-item-num\">1.3&nbsp;&nbsp;</span>Conséquences</a></span></li></ul></li><li><span><a href=\"#Objectif\" data-toc-modified-id=\"Objectif-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Objectif</a></span></li><li><span><a href=\"#Réprésentation-temporelle-d'un-signal\" data-toc-modified-id=\"Réprésentation-temporelle-d'un-signal-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Réprésentation temporelle d'un signal</a></span></li><li><span><a href=\"#Réprésentation-spectrale-d'un-signal\" data-toc-modified-id=\"Réprésentation-spectrale-d'un-signal-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>Réprésentation spectrale d'un signal</a></span></li><li><span><a href=\"#Filtrage-numérique-en-appliquant-la-fonction-de-transfert-à-chacune-des-harmoniques\" data-toc-modified-id=\"Filtrage-numérique-en-appliquant-la-fonction-de-transfert-à-chacune-des-harmoniques-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>Filtrage numérique en appliquant la fonction de transfert à chacune des harmoniques</a></span></li><li><span><a href=\"#Filtrage-numérique-en-appliquant-une-relation-de-récurrence\" data-toc-modified-id=\"Filtrage-numérique-en-appliquant-une-relation-de-récurrence-6\"><span class=\"toc-item-num\">6&nbsp;&nbsp;</span>Filtrage numérique en appliquant une relation de récurrence</a></span></li></ul></div>"]},{"cell_type":"markdown","metadata":{},"source":["> __Objectifs du BO :__\n",">\n","> - Capacité numérique : calculer, à l’aide d’un langage de programmation, la transformée de Fourier discrète d’un signal numérique\n","> - Calculer la transformée de Fourier discrète d’un signal à valeurs réelles en utilisant la fonction rfft de la bibliothèque numpy.fft (sa spécification étant donnée).\n"]},{"cell_type":"code","execution_count":null,"metadata":{"vscode":{"languageId":"html"}},"outputs":[],"source":["<div style=\"page-break-after: always;\"></div>"]},{"cell_type":"markdown","metadata":{},"source":["---\n","\n","## Documentation\n","\n","---"]},{"cell_type":"markdown","metadata":{},"source":["> Vous trouverez ci-après les `docstring` des fonctions à utiliser pour obtenir la transformée de Fourier discrète d'un signal 1D à valeurs réelles. Elles appartiennent à la librairie `scipy.fft`."]},{"cell_type":"markdown","metadata":{},"source":["### scipy.fft.fft :\n","\n","__scipy.fft.fft(x, n=None, axis=- 1, norm=None, overwrite_x=False, workers=None, *, plan=None)__\n","\n","Compute the 1-D discrete Fourier Transform for real input.\n","\n","This function computes the 1-D n-point discrete Fourier Transform (DFT) of a real-valued array by means of an efficient algorithm called the Fast Fourier Transform (FFT).\n","\n","Parameters :\n","\n","- xarray_like: Input array\n","- n :int, optional\n","  Number of points along transformation axis in the input to use.<br>\n","  If n is smaller than the length of the input, the input is cropped.<br>\n","  If it is larger, the input is padded with zeros.\n","  If n is not given, the length of the input along the axis specified by axis is used.\n","- axisint, optional<br>\n","  Axis over which to compute the FFT. If not given, the last axis is used.\n","- norm{“backward”, “ortho”, “forward”}, optional\n","  Normalization mode (see fft). Default is “backward”.\n","- overwrite_xbool, optional\n","  If True, the contents of x can be destroyed; the default is False. See fft for more details.\n","- workersint, optional\n","  Maximum number of workers to use for parallel computation.<br>\n","  If negative, the value wraps around from os.cpu_count(). See fft for more details.\n","- planobject, optional\n","  This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors.<br>\n","  It is currently not used in SciPy.\n","  \n","\n","\n","---\n","\n","__Notes :__\n","\n","FFT (Fast Fourier Transform) refers to a way the discrete Fourier Transform (DFT) can be calculated efficiently, by using symmetries in the calculated terms. The symmetry is highest when n is a power of 2, and the transform is therefore most efficient for these sizes. For poorly factorizable sizes, scipy.fft uses Bluestein’s algorithm [2] and so is never worse than O(n log n). Further performance improvements may be seen by zero-padding the input using next_fast_len.\n","\n","If x is a 1d array, then the fft is equivalent to :\n","\n","```python\n","    y[k] = np.sum(x * np.exp(-2j * np.pi * k * np.arange(n)/n))\n","```\n","    \n","The frequency term $f=k/n$ is found at $y[k]$. At $y[n/2]$ we reach the Nyquist frequency and wrap around to the negative-frequency terms. So, for an 8-point transform, the frequencies of the result are $[0, 1, 2, 3, -4, -3, -2, -1]$.<br>\n","To rearrange the fft output so that the zero-frequency component is centered, like $[-4, -3, -2, -1, 0, 1, 2, 3]$, use `fftshift`.\n","\n","Transforms can be done in single, double, or extended precision (long double) floating point.<br>\n","Half precision inputs will be converted to single precision and non-floating-point inputs will be converted to double precision.\n","\n","If the data type of x is real, a “real FFT” algorithm is automatically used, which roughly halves the computation time.<br>\n","To increase efficiency a little further, use rfft, which does the same calculation, but only outputs half of the symmetrical spectrum.<br>\n","If the data are both real and symmetrical, the dct can again double the efficiency, by generating half of the spectrum from half of the signal."]},{"cell_type":"markdown","metadata":{},"source":["### scipy.fft.rfft :\n","\n","__scipy.fft.rfft(x, n=None, axis=- 1, norm=None, overwrite_x=False, workers=None, *, plan=None)__\n","\n","Compute the 1-D discrete Fourier Transform for real input.\n","\n","This function computes the 1-D n-point discrete Fourier Transform (DFT) of a real-valued array by means of an efficient algorithm called the Fast Fourier Transform (FFT).\n","\n","Parameters :\n","\n","- xarray_like: Input array\n","- n :int, optional\n","  Number of points along transformation axis in the input to use.<br>\n","  If n is smaller than the length of the input, the input is cropped.<br>\n","  If it is larger, the input is padded with zeros.\n","  If n is not given, the length of the input along the axis specified by axis is used.\n","- axisint, optional<br>\n","  Axis over which to compute the FFT. If not given, the last axis is used.\n","- norm{“backward”, “ortho”, “forward”}, optional\n","  Normalization mode (see fft). Default is “backward”.\n","- overwrite_xbool, optional\n","  If True, the contents of x can be destroyed; the default is False. See fft for more details.\n","- workersint, optional\n","  Maximum number of workers to use for parallel computation.<br>\n","  If negative, the value wraps around from os.cpu_count(). See fft for more details.\n","- planobject, optional\n","  This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors.<br>\n","  It is currently not used in SciPy.\n","\n","---\n","  \n","__Notes :__\n","\n","When the DFT is computed for purely real input, the output is Hermitian-symmetric, i.e., the negative frequency terms are just the complex conjugates of the corresponding positive-frequency terms, and the negative-frequency terms are therefore redundant. This function does not compute the negative frequency terms, and the length of the transformed axis of the output is therefore `n//2 + 1`.\n","\n","When `X = rfft(x)` and $fs$ is the sampling frequency, $X[0]$ contains the zero-frequency term 0*fs, which is real due to Hermitian symmetry.\n","\n","If n is even, $A[-1]$ contains the term representing both positive and negative Nyquist frequency (+fs/2 and -fs/2), and must also be purely real. If n is odd, there is no term at fs/2; $A[-1]$ contains the largest positive frequency (fs/2*(n-1)/n), and is complex in the general case.\n","\n","If the input a contains an imaginary part, it is silently discarded."]},{"cell_type":"markdown","metadata":{},"source":["### Conséquences"]},{"cell_type":"markdown","metadata":{},"source":["Si le vecteur de base est réel, il est conseillé d'utiliser la version `rfft`.<br>\n","L'optimisation est effective mais pour la mettre en oeuvre il est souhaitable d'utiliser un nombre d'échantillons pairs."]},{"cell_type":"raw","metadata":{},"source":["<div style=\"page-break-after: always;\"></div>"]},{"cell_type":"markdown","metadata":{},"source":["---\n","\n","## Objectif\n","\n","---"]},{"cell_type":"markdown","metadata":{},"source":["Le but de cet exercice est : \n","\n","- de construire un signal périodique à partir d'une supersposition de signaux sinusoïdaux en vertu du thérorème de Fourier\n","- de tracer son spectre\n","- de réaliser un filtrage analogique en appliquant la fonction de transfert à chacune des harmoniques\n","- de réaliser un filtrage numérique à l'aide d'une relation de récurrence"]},{"cell_type":"markdown","metadata":{},"source":["    \n","On s'appuiera sur la trame d'un exercice dont l'énoncé est reproduit ci-dessous (attention, f0 fait ici référence à la fréquence fondamentale du signal créneau, à ne pas confondre avec la fréquence d'échantionnage qui sera notée fe)."]},{"cell_type":"markdown","metadata":{},"source":["__Librairies utiles :__"]},{"cell_type":"code","execution_count":1,"metadata":{"trusted":true},"outputs":[],"source":["import numpy as np \n","import matplotlib.pyplot as plt\n","from scipy.signal import square\n","plt.rcParams['axes.xmargin'] = 0\n","\n","from scipy.fft import rfft,irfft,rfftfreq\n","\n","%matplotlib inline\n"]},{"cell_type":"markdown","metadata":{},"source":["> __Note :__\n","> la librairie `fftpack` est désormais considérée comme obsolète.<br>\n","> L'usage de sa version moderne est recommandée."]},{"cell_type":"markdown","metadata":{"id":"RaU-caeNwqCX"},"source":["---\n","\n","## Réprésentation temporelle d'un signal\n","\n","---\n","\n","1. Rédiger ci-dessous un code en langage python permettant de tracer le signal :\n","$$s_1(t) \\;=A\\; \\cos{(2\\pi f_0 t)}$$\n","avec $A=1 V$, $f_0=1000 Hz$ entre $t_{min}=0$ et $t_{max}=5$ ms avec $N=1000$  points.\n"]},{"cell_type":"code","execution_count":2,"metadata":{"trusted":true},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["A = 1\n","f0 = 1000\n","def s1(t):\n","    return A*np.cos(2*np.pi*f0*t)\n","tmin = 0\n","tmax = 5e-3\n","N = 1000\n","times = np.linspace(tmin, tmax, N)\n","sig1 = s1(times)\n","plt.cla()\n","plt.title(\"s1(t) pour $t$ entre $0$ et $5ms$ \")\n","plt.plot(times, sig1)\n","plt.show()"]},{"attachments":{},"cell_type":"markdown","metadata":{},"source":["2. Rédiger ci-dessous un code en langage python permettant de tracer le signal :\n","$$s_2(t)\\;=A\\;\\cos{(2\\pi f_0 t)}+\\dfrac{A}{2}\\; \\sin{(2\\pi f_0 t)}$$ toujours avec $A=1 V$, $f_0=1000 Hz$ entre $t_{min}=0$ et $t_{max}=5$ ms avec $N=1000$  points."]},{"cell_type":"code","execution_count":3,"metadata":{"trusted":true},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["A = 1\n","f0 = 1E3\n","def s2(t):\n","    return A*np.cos(2*np.pi*f0*t) + (A/2)*np.sin(2*np.pi*f0*t)\n","tmin = 0\n","tmax = 5e-3\n","N = 1000\n","times = np.linspace(tmin, tmax, N)\n","sig2 = s2(times)\n","plt.clf()\n","plt.title(\"s2(t) pour $t$ entre $0$ et $5ms$ \")\n","plt.plot(times, sig2)\n","plt.show()"]},{"cell_type":"markdown","metadata":{},"source":["- Montrez que ce signal peut se mettre sous la forme :\n","$$s_2(t)\\;=B\\;\\cos{(2\\pi f_0 t + \\theta)}$$\n","Déterminez les valeurs de $(B,\\theta)$ et vérifiez l'identité avec le signal initial en traçant cette dernière expression.\n","\n","<br>\n","\n","- Enfin on définit le signal $e_1(t)$ comme :\n","$$e_1(t) = A + s_1(t) \\;=A\\; \\left( 1 + \\cos{(2\\pi f_0 t) } \\right)$$\n","Ajoutez la représentation de ce signal à vos traçés.\n","\n"]},{"cell_type":"markdown","metadata":{},"source":["3. Rédiger ci-dessous un code en langage python permettant de tracer un signal rectangulaire d'amplitude $A=1$ V et de fréquence $f_0=1000 Hz$, toujours entre $t_{min}=0$ et $t_{max}=5$ ms avec $N=1000$ points.<br>\n","Vous tracerez le signal créneau défini simplement en représentation temporelle, et sa version approchée construite par synthèse de Fourier. Vous vous limiterez aux 30 premières harmoniques.\n","\n","> On rappelle la décomposition en série de Fourier d'un signal rectangulaire impair : $$s_3(t)=\\cfrac{4A}{\\pi}\\sum_{k=0}^{\\infty}\\cfrac{\\sin{\\left(2 \\pi [2 k + 1] f_0 t\\right)}}{2 k + 1}$$"]},{"cell_type":"code","execution_count":4,"metadata":{"trusted":true},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["C = A*(1+0.5j)\n","B = np.abs(C)\n","theta = np.angle(C)\n","def s2b(t) :\n","    return B*np.cos(2*np.pi*f0*t + theta)\n","\n","tmin = 0\n","tmax = 5e-3\n","N = 1000\n","times = np.linspace(tmin, tmax, N)\n","sig2b = s2b(times)\n","plt.clf()\n","plt.title(\"s2'(t) pour $t$ entre $0$ et $5ms$ \")\n","plt.plot(times, sig2b)\n","plt.show()"]},{"cell_type":"code","execution_count":5,"metadata":{"trusted":true},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure 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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["A = 1\n","f0 = 1E3\n","#def crenau(t):\n","#    return A*square(2*np.pi*f0*t)\n","\n","def crenau(t, f):\n","    u = np.remainder(f*t, 1)\n","    return 1-2*np.heaviside(u-0.5, 0)\n","\n","\n","def crenau_bis(t):\n","    res = 0\n","    for k in range(30):\n","        res += np.sin(2*np.pi*(2*k+1)*f0*t)/(2*k+1)\n","    return 4*(A/np.pi) * res\n","tmin = 0\n","tmax = 5e-3\n","N = 1000\n","times = np.linspace(tmin, tmax, N)\n","cren = crenau(times, f0)\n","plt.clf()\n","plt.title(\"Crénau parfait pour $t$ entre $0$ et $5ms$ \")\n","plt.plot(times, cren)\n","plt.show()\n","plt.title(\"Crénau à 30 harmoniques pour $t$ entre $0$ et $5ms$\")\n","crenb = crenau_bis(times)\n","plt.plot(times, crenb)\n","plt.show()"]},{"cell_type":"code","execution_count":null,"metadata":{"vscode":{"languageId":"html"}},"outputs":[],"source":["<div style=\"page-break-after: always;\"></div>"]},{"cell_type":"markdown","metadata":{},"source":["---\n","\n","## Réprésentation spectrale d'un signal\n","\n","---\n","\n","4. Calculer et afficher  :\n"," - la période d'échantillonnage $T_e$,\n"," - la fréquence d'échantillonnage $f_e$\n"," - et la résolution spectrale $\\Delta f_{min}$."]},{"cell_type":"code","execution_count":6,"metadata":{"trusted":true},"outputs":[{"name":"stdout","output_type":"stream","text":["Te =5.000E-06 s,fe = 2.000E+05 Hz, Delta f_min = 2.000E+02 Hz\n"]}],"source":["# Code déjà rempli\n","# période d'échantillonnage : \n","Te = (tmax-tmin)/N\n","# fréquence d'échantillonnage:\n","fe = 1/Te\n","# résolution spectrale\n","Deltaf = fe/N\n","print(f'Te ={Te:1.3E} s,fe = {fe:1.3E} Hz, Delta f_min = {Deltaf:1.3E} Hz')"]},{"cell_type":"markdown","metadata":{},"source":["5. A partir des expressions temporelles, déterminez les spectres des signaux précédents.<br>\n","Représenter ces derniers en limitant l'axe des fréquences à $f_{max}=10000 Hz$."]},{"cell_type":"markdown","metadata":{},"source":["Spectre de $s_1(t)$: $$S_1(f) = \\cfrac{A}{2}$$\n","Spectre de $s_2(t)$: $$S_2(f) = \\cfrac{A}{2}$$\n","Spectre de $s_{2b}(t)$: $$S_{2b}(f) = \\cfrac{A}{2}$$\n","Spectre de $creneau(t)$: $$S_{creneau}(f) = \\sum_{k=0}^\\infty \\frac{A}{2k+1}$$\n"]},{"cell_type":"markdown","metadata":{},"source":["6. Rédiger ci-dessous un code en langage python permettant de tracer le spectre des différents signaux précédents en utilisant la fonction `rfft` et en limitant l'axe des fréquences à $f_{max}=10000 Hz$."]},{"cell_type":"code","execution_count":7,"metadata":{"trusted":true},"outputs":[],"source":["def affiche_spectre(sig, fe, fmax):\n","    N = len(sig)\n","    sig_fft = rfft(sig)\n","    freqs = rfftfreq(N, 1/fe)\n","    plt.clf()\n","    plt.title(\"Spectre du signal\")\n","    plt.plot(freqs, np.abs(sig_fft))\n","    plt.xlim(0, fmax)\n","    plt.show()\n","    return sig_fft"]},{"cell_type":"code","execution_count":8,"metadata":{"scrolled":true,"trusted":true},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure 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","text/plain":["<Figure 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","text/plain":["<Figure 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","text/plain":["<Figure 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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["spsig1 = affiche_spectre(sig1, fe, 10E3)\n","spsig2 = affiche_spectre(sig2, fe, 10E3)\n","spsig2b = affiche_spectre(sig2b, fe, 10E3)\n","spcren = affiche_spectre(cren, fe, 10E3)\n","spcrenb = affiche_spectre(crenb, fe, 10E3)\n","\n"]},{"cell_type":"raw","metadata":{},"source":["<div style=\"page-break-after: always;\"></div>"]},{"cell_type":"markdown","metadata":{},"source":["---\n","\n","## Filtrage numérique en appliquant la fonction de transfert à chacune des harmoniques\n","\n","---\n","\n","7. Reproduire l'effet du filtre passe-base d'ordre 1 sur le signal créneau, de fonction de transfert :\n","$$\\underline{H}=\\cfrac{1}{1+j\\cfrac{f}{f_c}}\\qquad avec\\qquad fc=0.1*f_0$$\n","\n","Le gain et la phase sont donnés par :\n","$$G(f)=\\cfrac{1}{\\sqrt{1+\\left(\\cfrac{f}{f_c}\\right)^2}} \\qquad et \\qquad \\varphi(f)=- argument\\left(1 + j\\cfrac{f}{f_c}\\right)$$"]},{"cell_type":"code","execution_count":9,"metadata":{"trusted":true},"outputs":[{"name":"stderr","output_type":"stream","text":["/var/folders/f3/68h644h17rzcj7c0b9062v240000gn/T/ipykernel_3623/297937851.py:13: RuntimeWarning: divide by zero encountered in log\n","  plt.plot(np.log(freqs), G(freqs))\n"]},{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"},{"name":"stderr","output_type":"stream","text":["/var/folders/f3/68h644h17rzcj7c0b9062v240000gn/T/ipykernel_3623/297937851.py:15: RuntimeWarning: divide by zero encountered in log\n","  plt.plot(np.log(freqs), phi(freqs))\n"]},{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAiMAAAGdCAYAAADAAnMpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy88F64QAAAACXBIWXMAAA9hAAAPYQGoP6dpAABAuElEQVR4nO3deVxU5eIG8GdmYIZ92JFNAXdREUUJTbsWZlq0p6U3DZduZVZyW6RSM01avdZPzau5lbmUqS2aZt7KJUsBUXFHVBBZZRkYYIaZOb8/KIoUZQx4Z3m+n898cF7O4TxMwDyd5T0ySZIkEBEREQkiFx2AiIiI7BvLCBEREQnFMkJERERCsYwQERGRUCwjREREJBTLCBEREQnFMkJERERCsYwQERGRUA6iAzSHyWTCpUuX4O7uDplMJjoOERERNYMkSaisrERQUBDk8qb3f1hFGbl06RJCQ0NFxyAiIqIbkJubi5CQkCY/bxVlxN3dHUD9N+Ph4SE4DRERETWHRqNBaGhow/t4U6yijPx+aMbDw4NlhIiIyMpc7xQLs09g3b17NxISEhAUFASZTIYtW7Zcdx2dTodXXnkFHTp0gEqlQlhYGFasWGHupomIiMgGmb1nRKvVIioqChMmTMD999/frHVGjRqFwsJCLF++HJ06dUJ+fj5MJpPZYYmIiMj2mF1GRowYgREjRjR7+e3bt+Onn35CdnY2vL29AQBhYWHmbpaIiIhsVKvPM/LVV18hJiYGb7/9NoKDg9GlSxc8//zzqKmpaXIdnU4HjUbT6EFERES2qdVPYM3OzsbevXvh5OSEzZs3o6SkBE899RQuX76MlStXXnWdlJQUzJ49u7WjERERkQVo9T0jJpMJMpkMn376KQYMGICRI0di/vz5WL16dZN7R5KTk1FRUdHwyM3Nbe2YREREJEir7xkJDAxEcHAw1Gp1w1j37t0hSRIuXryIzp07X7GOSqWCSqVq7WhERERkAVp9z8igQYNw6dIlVFVVNYydPn0acrn8mrOxERERkX0wu4xUVVUhIyMDGRkZAIBz584hIyMDOTk5AOoPsYwbN65h+TFjxsDHxweJiYk4fvw4du/ejRdeeAETJkyAs7Nzy3wXREREZLXMLiOpqamIjo5GdHQ0ACApKQnR0dGYOXMmACA/P7+hmACAm5sbdu7cifLycsTExGDs2LFISEjABx980ELfAhEREVkzmSRJkugQ16PRaKBWq1FRUcHp4ImIiKxEc9+/W/2cESIiIqJrsYob5REREZEYJpMEncGE2jojauqMf/pYP1b7279rGv79xzLlFc2btJRlhIiIyAZIkoSaOiOqdAZU64zQ6g2o1v/luc4Ard4Ira7+c1qdAVq9AVqdEdV/+vjncqEz3Pi95Ey66mYtxzJCRERkAWrrjNDU1kFTY0BlbR00tb99/O15Za0Bmt8/1lz5vEpvQGufBeqokMHJUQEnRwWcHRVwcpTD2VEBVcOY/E+fU0Cqq8brC67/dVlGiIiIWpDJJEFTW4ey6jqUVetRXq1Hmfb3f//xsVSrbzT2d/ZA/JlMBrgqHeCiVMBN5QAXlQIuSge4KhVwUTnATVk/5vrbRzeVQ6PPuyj/KBqNi4cCCrnMrCwajQavN2M5lhEiIqLrMBhNKNXqUVylQ3GlDiVVepRU6VBSqUNJlQ7FVTqUVNaPlVXrYbrBPRQyGeCucoCHsyPcnRzh4eRQ/9HZAR5/eu7u9Psy9ePuv427qRzg5CiHTGZeaRCNZYSIiOyWySShtFqPgopaFFTUIl9Ti8KKWuRX1KJQU4viyvqiUVatN/sQiKtSAU8XJbxcHeHloqz/t0v9v71cHOHl2nhM7eIIN6UD5GbufbAFLCNERGSzKmrqcLGsGhfLanCxrAb55TUo0NQXjwJNfeGoMzavZchlgLerCr5uSvi5q+DnpoKve/1zXzdVw8PHTQlPF0eoHBSt/N3ZDpYRIiKyWlU6Q33ZKK1BbkPpqEZuaf1HTa3hul9DJgN83VQIVDshwMMJgWontFM7oZ2HE/zdneDrXl82vFyUZp8zQc3DMkJERBatts6InNJqZBdrcf6yFueKtThXosW5y1oUV+quu76PqxIhXs4I8XJBkOfvhcMZ7dQqtFM7w99dBUcF5wAViWWEiIgsQkmVDqcLKnG6sBJnfyse2cVaXKqoueb5Gp4ujvVlw9MFod71peP3j8GeznBV8a3O0vG/EBERtanyaj1OF1bhVGElzhRW4lRBJc4UVaFUq29yHXeVA8L9XBHu64owH1dE+NV/DPN1hdrZsQ3TU2tgGSEiolZhMknIKa3GsUsaZF6qwLFLGpzI1zR5aEUmA9p7u6Czvzs6+bsh4rfyEe7rCh9XpdVdrkrNxzJCRER/m8FowtliLTLzKhrKx4lLGlTqrn4CabCnM7oEuKFLgHvDo5O/G5yVvALFHrGMEBGR2Yo0tUjPKceh3DIcyinH0YsVqKkzXrGc0kGO7u3c0SNIjZ7BHuge6IEuAe5w43kc9Cf8aSAiomvSGYzIzNPgUE4ZDuWWIyOnHHnlNVcs56ZyQI9AD0QGeyDyt/LR0c+NV6rQdbGMEBFRI7V1RqRfKMMv50rxa/ZlHMoth/4v902Ry4AuAe6Ibu+F6Pae6NveExG+bnY5eyj9fSwjRER2rlpvQNqFMvyaXYpfz13G4dwK6I2Ny4ePq7KheES390TvEE8eaqEWw58kIiI7YzJJOJ6vwe4zxdh9uhhpF8qumBI9wEOF2HAfxEZ4IzbcBx39XHk1C7UalhEiIjtQpKnF7jMl2HOmGHvPlODyX+b0CPZ0Rmy4d0P56ODjwvJBbYZlhIjIBplMEo7mVeD7E4XYebwQJwsqG33eValAXEdfDOniiyGd/Vg+SCiWESIiG6EzGPHz2cvYebwQu04UolDzx+RiMhnQK1iNIZ39MLizL/p28OJVLmQxWEaIiKxYlc6AXScKsT2zALtPF0Or/2OuD1elArd09cOwHgG4pYs/vF2VApMSNY1lhIjIylTrDdh1ogjfHLmEH04VN7rsNsBDhfjuARjWIwBxHX2gcuCMpmT5WEaIiKxAbZ0RP5wswjdH8/G/E0WNZjuN8HXFyF6BuD0yAL2C1Tz3g6wOywgRkYWSJAlpF8rwRfpFfHM4v9F9Xtp7u+Cu3oG4q3cQuge6s4CQVWMZISKyMBfLqrE5PQ9fpF/E+cvVDeNBaifcFRWEu3oHcg8I2RSWESIiC6AzGLE9swDrD+Rif/blhnEXpQIjegbigX7BuCnch9Otk01iGSEiEujCZS3WHsjB56kXUfqnicjiInzwQL8QjOjZDq6cdp1sHH/CiYjaWJ3RhF0nivDprxew50xJw3g7Dyc8PCAUD/YLQYiXi8CERG2LZYSIqI2UV+ux9kAOPv75Ago0tQDqJyO7pYsfxsZ2wNCufnDgRGRkh1hGiIhaWXZxFVbsO4cv0vIaLsn1dVNiVEwoHhnQHqHe3AtC9o1lhIioFUiShP3Zl7F8zznsOlnUMN490AOTbg7HXVGBnJCM6DcsI0RELUiSJPzvZBEW/pCFQznlDePx3f0x4eZwxEX48JJcor9gGSEiagFGk4TtmQVY+EMWTuRrAAAqBzkeignBhEHhiPBzE5yQyHKZfabU7t27kZCQgKCgIMhkMmzZsqXZ6+7btw8ODg7o06ePuZslIrJIdUYTvki7iGH/+QlT1qbjRL4GrkoF/jUkAnteGoq59/ZiESG6DrP3jGi1WkRFRWHChAm4//77m71eeXk5xo0bh9tuuw2FhYXmbpaIyKKYTBK+PnIJ83eexoXfZklVOzvisYFhSBwUBk8X3iGXqLnMLiMjRozAiBEjzN7QE088gTFjxkChUJi1N4WIyJJIkoSdxwvx3nencaqwEkD9lTGTBkfgnzd1gBsnKCMyW5v81qxcuRLZ2dlYs2YN5s6de93ldToddDpdw3ONRtOa8YiImuXnrBK8veMUMnLLAQAeTg741y0dkTgoDC5KlhCiG9Xqvz1nzpzB9OnTsWfPHjg4NG9zKSkpmD17disnIyJqnlMFlZi79XjDbKnOjgpMuDkMjw/uCLWLo+B0RNavVcuI0WjEmDFjMHv2bHTp0qXZ6yUnJyMpKanhuUajQWhoaGtEJCJq0uUqHebvPI11B3JgkgClQo4xse0xZWgn+LmrRMcjshmtWkYqKyuRmpqKQ4cO4emnnwYAmEwmSJIEBwcHfPfdd7j11luvWE+lUkGl4i86EYmhMxixat95LPxfFip1BgDAyF7tMP2O7mjvw9lSiVpaq5YRDw8PHD16tNHY4sWL8b///Q8bN25EeHh4a26eiMgskiRhx7FCzNt2Ajml9VfI9Az2wIw7eyA2wkdwOiLbZXYZqaqqQlZWVsPzc+fOISMjA97e3mjfvj2Sk5ORl5eHjz/+GHK5HD179my0vr+/P5ycnK4YJyIS6XyJFjO+zGw4L8TfXYUXhnfFA31DIJdzxlSi1mR2GUlNTcXQoUMbnv9+bsf48eOxatUq5OfnIycnp+USEhG1Ip3BiP/+lI2FP2RBbzBB6SDH44Mj8OQ/OsKVl+kStQmZJEmS6BDXo9FooFarUVFRAQ8PD9FxiMhG/JxVgle3ZCK7RAsAGNzZF6/f0xPhvq6CkxHZhua+f7P2E5HdKdXqMeeb49h8KA8A4Oeuwoy7eiChdyBvYkckAMsIEdmV7Zn5eHVLJkqq9JDJgHE3dcC/h3eFhxPnCyEShWWEiOzC5SodZn11DN8cyQcAdAlww9sPRqFPqKfYYETEMkJEtm/b0XzM2JKJy1o9FHIZnrylI6be1gkqB4XoaEQElhEismGlWj1mbMnE1qP1e0O6Brjj3Yei0CtELTgZEf0ZywgR2aS9Z0qQ9FkGiip1UMhlmPKPjphyK/eGEFkilhEisik6gxHv7jiFZXvOAQA6+rni/Yej0TOYe0OILBXLCBHZjKyiKjyz7hCO52sAAP+8qT1eGdkDzkruDSGyZCwjRGQTPjuYi5lfZaK2zgQvF0e8/WAUhvUIEB2LiJqBZYSIrFqN3ogZX2ZiY9pFAPWzqL73UBT8PZwEJyOi5mIZISKrdba4Ck+tScepwkrIZcC/b++KJ2/pyBvbEVkZlhEiskpfH76E6V8cgVZvhK+bCh880gcDO/qKjkVEN4BlhIisSp3RhDe2nsCqn88DAGLDvfF/j0TzsAyRFWMZISKrUarV46lP0/BLdikA4Kl/dETSsC5wUMgFJyOiv4NlhIiswol8DSZ/nIqLZTVwVSrwn9F9cHtkO9GxiKgFsIwQkcXbnpmPpM8Oo1pvRAcfFywbF4MuAe6iYxFRC2EZISKLZTJJeH/XGby/6wwA4OZOvlg4JhqeLkrByYioJbGMEJFFqq0zYtqGDHybWQAAmDAoHC+P7MbzQ4hsEMsIEVmcUq0ek1YfRHpOOZQKOebe1xOjYkJFxyKiVsIyQkQW5cJlLR5beRDnSrTwcHLAsnExiI3wER2LiFoRywgRWYyM3HJMXHUQl7V6BHs6Y/WE/ujkzxNViWwdywgRWYSdxwsxdV06autM6BnsgRXj+3MiMyI7wTJCRMJ9vP88XvvqGEwSMLSrHxaO6QtXFf88EdkL/rYTkTCSJOE/O0/jg/9lAQAeGRCKOff05BUzRHaGZYSIhDCZJLz+zfGGe8wkDeuCqbd2gkzGO+4S2RuWESJqcwajCS9uPIJNh/IAAHPuicSjcWFiQxGRMCwjRNSmauuMmLruEHYeL4RCLsN7D0Xh3uhg0bGISCCWESJqMzV6IyZ9fBD7si5D6SDH4jF9Ed8jQHQsIhKMZYSI2kS13oAJqw7il+xSuCoVWDY+BgM7+oqORUQWgGWEiFpdlc6ACSsP4sD5UripHLB6Qn/06+AtOhYRWQiWESJqVZW1dUhceRCpF8rgrnLAxxMHILq9l+hYRGRBWEaIqNVoauvw2IoDSM8ph4eTAz6ZGIuoUE/RsYjIwrCMEFGrqNIZMH7FARzKKYfa2RFrJsaiV4hadCwiskAsI0TU4mr0RkxYdRCHcsrh6VJfRHoGs4gQ0dVxzmUialE6gxGPf5KKA+dK4a5ywCcTWESI6NrMLiO7d+9GQkICgoKCIJPJsGXLlmsuv2nTJgwbNgx+fn7w8PBAXFwcduzYcaN5iciC1RlNeHrtIew5UwJnRwVWJvbnoRkiui6zy4hWq0VUVBQWLVrUrOV3796NYcOGYdu2bUhLS8PQoUORkJCAQ4cOmR2WiCyX0SRh2oYM7DxeCKWDHMvHxyAmjJfvEtH1ySRJkm54ZZkMmzdvxr333mvWepGRkRg9ejRmzpzZrOU1Gg3UajUqKirg4eFxA0mJqDWZTBJe+uIIPk+7CEeFDEsfjcHQbv6iYxGRYM19/27zE1hNJhMqKyvh7d30/zHpdDrodLqG5xqNpi2iEdENenP7SXyedhFyGfDBw9EsIkRkljY/gfXdd99FVVUVRo0a1eQyKSkpUKvVDY/Q0NA2TEhE5li6+yyW7s4GALz9YBRG9AoUnIiIrE2blpG1a9di9uzZ+Oyzz+Dv3/T/OSUnJ6OioqLhkZub24Ypiai5NqVfxLxtJwEAySO64cF+IYITEZE1arPDNOvXr8ekSZPw+eefIz4+/prLqlQqqFSqNkpGRDfih1NFeHHjEQDApJvD8fiQCMGJiMhatcmekXXr1iExMRHr1q3DnXfe2RabJKJWdCinDE+tSYfBJOHePkF4eWR3yGQy0bGIyEqZvWekqqoKWVlZDc/PnTuHjIwMeHt7o3379khOTkZeXh4+/vhjAPWHZsaPH4/3338fsbGxKCgoAAA4OztDreb8A0TWJquoChNWHURNnRFDuvjh7QejIJeziBDRjTN7z0hqaiqio6MRHR0NAEhKSkJ0dHTDZbr5+fnIyclpWH7p0qUwGAyYMmUKAgMDGx7PPvtsC30LRNRWiiprMX7FAZRV1yEqRI0Px/aF0oETORPR3/O35hlpK5xnhEi8Gr0RDy/7BYdzyxHm44IvnhwIHzee20VETWvu+zf/l4aIrstkkpD0WQYO59bf+G5l4gAWESJqMSwjRHRdb+84hW8zC+CokOG//+yHcF9X0ZGIyIawjBDRNW04mIMlP50FALx5f2/ERvgITkREtoZlhIiatC+rBK9szgQAPHNrJzzASc2IqBWwjBDRVWUVVeKJNWkwmCTcHRWEacO6iI5ERDaKZYSIrlCq1SNx1UFU1hrQr4MX3n6wNyc1I6JWwzJCRI0YjCY8vTYduaU1CPV2xtJH+8HJUSE6FhHZMJYRImok5duT+PnsZbgoFfhoXH9ewktErY5lhIgabEq/iOV7zwEA5o+KQtd27oITEZE9YBkhIgDAkYvlmL7pKABg6q2dcEfPQMGJiMhesIwQEYordfjXJ2nQG0y4rZs/psXzyhkiajssI0R2rs5owpRP05FfUYsIP1f85+E+vAsvEbUplhEiOzfnm+M4cL4UbioHLH00Bh5OjqIjEZGdYRkhsmOfHczFx/svAAD+M7oPOvm7CU5ERPaIZYTITmXmVeDVLfVTvU+L74JhPQIEJyIie8UyQmSHKmrq8NSn6dAbTYjv7o+pt3YSHYmI7BjLCJGdkSQJL248jJzSaoR4OeO9h3jCKhGJxTJCZGdW7DuPHccKoVTIsXhsX6hdeMIqEYnFMkJkR9JzypCy7QQA4NW7uqN3iKfYQEREYBkhshtlWj2e/jQdBpOEO3sH4tGbOoiOREQEgGWEyC6YTBKSPsvApYpahPu64s37e0Em43kiRGQZWEaI7MCS3Wfxw6liqBzkWDSmL9w5sRkRWRCWESIb90v2Zby74xQA4PV7ItEjyENwIiKixlhGiGxYcaUOz6w7BJME3N83GKNiQkVHIiK6AssIkY0ymST8+/PDKKrUobO/G+be25PniRCRRWIZIbJRK38+j92ni+HkWD+fiIvSQXQkIqKrYhkhskHHL2nw1rcnAQCv3tkDnQPcBSciImoaywiRjamtM+LZ9Yd+u+9MAMbGthcdiYjomlhGiGzMG1tP4ExRFfzcVXjrAc4nQkSWj2WEyIZ8f7wQn/xyAQAwf1QUfNxUghMREV0fywiRjSjS1OLFL44AACbdHI7Bnf0EJyIiah6WESIb8PtlvKVaPXoEeuCFO7qKjkRE1GwsI0Q2YMW+c9hzpgROjnJ88EgfqBwUoiMRETUbywiRlTt2qQJvb6+f7v3VO3ugkz8v4yUi68IyQmTFavRGPLs+g5fxEpFVM7uM7N69GwkJCQgKCoJMJsOWLVuuu86PP/6Ivn37QqVSoVOnTli1atUNRCWiv5q37QSyeBkvEVk5s8uIVqtFVFQUFi1a1Kzlz507hzvvvBNDhw5FRkYGnnvuOUyaNAk7duwwOywR/eHHU0W8jJeIbILZN6sYMWIERowY0ezllyxZgvDwcLz33nsAgO7du2Pv3r34z3/+g+HDh5u7eSICUFFTh+lfHAUAPDYwjJfxEpFVa/VzRvbv34/4+PhGY8OHD8f+/fubXEen00Gj0TR6ENEfZn99DAWaWoT7uuKlO7qJjkNE9Le0ehkpKChAQEBAo7GAgABoNBrU1NRcdZ2UlBSo1eqGR2hoaGvHJLIa3x0rwKb0PMhlwLsPRcFZyct4ici6WeTVNMnJyaioqGh45Obmio5EZBFKtXq8vLn+8MzkIRHo18FLcCIior/P7HNGzNWuXTsUFhY2GissLISHhwecnZ2vuo5KpYJKxZPxiP5qxpeZKKnSo7O/G6bFdxEdh4ioRbT6npG4uDjs2rWr0djOnTsRFxfX2psmsinfHLmErUfyoZDLMH9UHzg58vAMEdkGs8tIVVUVMjIykJGRAaD+0t2MjAzk5OQAqD/EMm7cuIbln3jiCWRnZ+PFF1/EyZMnsXjxYnz22WeYNm1ay3wHRHagqLIWM7ZkAgCmDO2EXiFqwYmIiFqO2WUkNTUV0dHRiI6OBgAkJSUhOjoaM2fOBADk5+c3FBMACA8Px9atW7Fz505ERUXhvffew0cffcTLeomaSZIkvLwpE2XVdegR6IGnh3YSHYmIqEXJJEmSRIe4Ho1GA7VajYqKCnh4eIiOQ9Smvki7iH9/fhiOChm+nnozurXj7wARWYfmvn9b5NU0RFQvv6IGr319DADwXHwXFhEiskksI0QWSpIkvPTFUVTWGhAV6ol/DYkQHYmIqFWwjBBZqPUHc7H7dDFUDnK891AUHBT8dSUi28S/bkQWKLe0GnO/OQ4AeGF4V3TydxOciIio9bCMEFkYSZIwfdMRaPVG9A/zQuKgcNGRiIhaFcsIkYX5PPUi9mVdhpOjHO88GAWFXCY6EhFRq2IZIbIgRZpazNlaf3gmaVgXhPm6Ck5ERNT6WEaILMjML4+hstaA3iFqTODhGSKyEywjRBbi26P52H6sAA5yGd56oDevniEiu8G/dkQWoKK6DjO+rJ/c7Ml/dET3QE5uRkT2g2WEyALM3XocJVU6dPRzxdO38t4zRGRfWEaIBNt7pgSfp12ETAa89UBvqBwUoiMREbUplhEigar1BkzfdAQAMO6mDogJ8xaciIio7bGMEAn03nencbGsBsGeznjhjm6i4xARCcEyQiRIek4ZVuw7BwB4476ecFM5CE5ERCQGywiRAHqDCdO/OAJJAu6PDsY/uvqLjkREJAzLCJEAi3/MwunCKvi4KjHjrh6i4xARCcUyQtTGThdWYtEPWQCA1+6OhJerUnAiIiKxWEaI2pDRJOHFjUdQZ5QQ390fd/UOFB2JiEg4lhGiNrTq5/PIyC2Hu8oBc+7tCZmMd+QlImIZIWojuaXVeHfHKQDA9JHdEKh2FpyIiMgysIwQtQFJkvDy5qOoqTMiNtwbj/RvLzoSEZHFYBkhagNfHb6EPWdKoHSQI+X+XpDLeXiGiOh3LCNEray8Wo/Xvz4OAJg6tBMi/NwEJyIisiwsI0StLGXbSVzW6tHZ3w3/uqWj6DhERBaHZYSoFf2afRkbUnMBAPPu7wWlA3/liIj+in8ZiVqJzmDEy5uPAgAeGdAe/XlHXiKiq2IZIWolS37MxtliLXzdVJjOO/ISETWJZYSoFZwtrmqY8n1mQg+oXRwFJyIislwsI0QtTJIkvLL5KPRGE27p4ocETvlORHRNLCNELWxj2kX8kl0KJ0c55nLKdyKi62IZIWpBl6t0eGPbCQDAtPguCPV2EZyIiMjysYwQtaA3tp5AeXUdurVzx4Sbw0XHISKyCiwjRC1k75kSbDqUB5kMePOB3nBU8NeLiKg5+NeSqAXU1hnx6pb6OUXG3dQBfUI9xQYiIrIiN1RGFi1ahLCwMDg5OSE2NhYHDhy45vILFixA165d4ezsjNDQUEybNg21tbU3FJjIEi38XxbOX65GOw8nPD+8q+g4RERWxewysmHDBiQlJWHWrFlIT09HVFQUhg8fjqKioqsuv3btWkyfPh2zZs3CiRMnsHz5cmzYsAEvv/zy3w5PZAlOF1ZiyU9nAQCv3R0JdyfOKUJEZA6zy8j8+fMxefJkJCYmokePHliyZAlcXFywYsWKqy7/888/Y9CgQRgzZgzCwsJw++2345FHHrnu3hQia2AySUjedBQGk4T47gEYHhkgOhIRkdUxq4zo9XqkpaUhPj7+jy8glyM+Ph779++/6joDBw5EWlpaQ/nIzs7Gtm3bMHLkyCa3o9PpoNFoGj2ILNG6gzlIu1AGV6UCr98TyTlFiIhugIM5C5eUlMBoNCIgoPH//QUEBODkyZNXXWfMmDEoKSnBzTffDEmSYDAY8MQTT1zzME1KSgpmz55tTjSiNldUWYs3v63/uf/37V0R5OksOBERkXVq9atpfvzxR8ybNw+LFy9Geno6Nm3ahK1bt2LOnDlNrpOcnIyKioqGR25ubmvHJDLb618fR2WtAb1D1Bg/MEx0HCIiq2XWnhFfX18oFAoUFhY2Gi8sLES7du2uus6MGTPw6KOPYtKkSQCAXr16QavV4vHHH8crr7wCufzKPqRSqaBSqcyJRtSmfjhVhG+O5EMuA+bd1wsKOQ/PEBHdKLP2jCiVSvTr1w+7du1qGDOZTNi1axfi4uKuuk51dfUVhUOhUACov6EYkbWp1hswY0smAGDCoHD0DFYLTkREZN3M2jMCAElJSRg/fjxiYmIwYMAALFiwAFqtFomJiQCAcePGITg4GCkpKQCAhIQEzJ8/H9HR0YiNjUVWVhZmzJiBhISEhlJCZE0WfH8GF8tqEOzpjGnDuoiOQ0Rk9cwuI6NHj0ZxcTFmzpyJgoIC9OnTB9u3b284qTUnJ6fRnpBXX30VMpkMr776KvLy8uDn54eEhAS88cYbLfddELWRY5cqsHzvOQDAnHsj4aoy+1eIiIj+QiZZwbESjUYDtVqNiooKeHh4iI5DdspoknDf4n04crECd/YOxKIxfUVHIiKyaM19/+a9aYiaafXP53HkYgXcnRwwK6GH6DhERDaDZYSoGS6V1+C9704BAKaP6AZ/dyfBiYiIbAfLCNF1SJKEmV8eg1ZvREwHLzzSv73oSERENoVlhOg6dhwrwPcnCuGokGHe/b0g55wiREQtimWE6Bo0tXWY9dUxAMC/hnRElwB3wYmIiGwPywjRNbyz/RQKNTqE+bjg6Vs7iY5DRGSTWEaImpB2oQxrfr0AoH7KdydHTtJHRNQaWEaIrqLOaMLLm45CkoAH+oZgYCdf0ZGIiGwWywjRVSzbk41ThZXwcnHEK3d2Fx2HiMimsYwQ/cWFy1q8//0ZAMCrd/aAt6tScCIiItvGMkL0J5Ik4ZXNmdAZTBjUyQf39w0WHYmIyOaxjBD9yZaMPOzNKoHSQY659/aCTMY5RYiIWhvLCNFvyrR6zPnmBADgmVs7IdzXVXAiIiL7wDJC9Jt5206gVKtHlwA3PD6ko+g4RER2g2WECMDPZ0vwedpFAEDK/b2gdOCvBhFRW+FfXLJ7tXVGvLI5EwAwNrY9+nXwFpyIiMi+sIyQ3Vv8QxbOlWjh567Ci3d0Ex2HiMjusIyQXTtTWIkPfzoLAHgtIRJqZ0fBiYiI7A/LCNktk0nCy5uPos4o4dZu/hjZq53oSEREdollhOzW+oO5OHi+DC5KBV6/J5JzihARCcIyQnapqLIWKd/WzymSNKwLQrxcBCciIrJfLCNkl17/+jgqaw3oGeyBxwaGiY5DRGTXWEbI7uw8XohvjuRDLgNS7usNBwV/DYiIROJfYbIrFTV1eGXzUQDA5CER6BWiFpyIiIhYRsiuzNt6AkWVOoT7umJafBfRcYiICCwjZEf2ZZVgQ2ouAODN+3vByVEhOBEREQEsI2QnqvUGTN90BADw6E0dEBvhIzgRERH9jmWE7MI7O04ht7QGQWonvDSCU74TEVkSlhGyeWkXyrDq5/MAgHn394KbykFsICIiaoRlhGyazmDES18cgSQB9/cNxj+6+ouOREREf8EyQjbt/3ZlIauoCr5uKsy8q4foOEREdBUsI2Szjl2qwJLf7sg7555IeLooBSciIqKrYRkhm2QwmvDSF0dgMEm4I7IdRvQKFB2JiIiawDJCNmnpnmxk5mmgdnbE6/dGio5DRETXwDJCNudscRUWfH8GADDjrh7wd3cSnIiIiK7lhsrIokWLEBYWBicnJ8TGxuLAgQPXXL68vBxTpkxBYGAgVCoVunTpgm3btt1QYKJrMZkkTP/iCPQGE4Z08cMDfYNFRyIiouswe8KFDRs2ICkpCUuWLEFsbCwWLFiA4cOH49SpU/D3v/KySb1ej2HDhsHf3x8bN25EcHAwLly4AE9Pz5bIT9TI6v3ncfB8GVyVCsy7rydkMpnoSEREdB0ySZIkc1aIjY1F//79sXDhQgCAyWRCaGgopk6diunTp1+x/JIlS/DOO+/g5MmTcHR0vKGQGo0GarUaFRUV8PDwuKGvQbbvbHEVRr6/BzqDCXPuicSjcWGiIxER2bXmvn+bdZhGr9cjLS0N8fHxf3wBuRzx8fHYv3//Vdf56quvEBcXhylTpiAgIAA9e/bEvHnzYDQam9yOTqeDRqNp9CC6FoPRhKTPDkNnMGFwZ1+Mje0gOhIRETWTWWWkpKQERqMRAQEBjcYDAgJQUFBw1XWys7OxceNGGI1GbNu2DTNmzMB7772HuXPnNrmdlJQUqNXqhkdoaKg5MckOLfnpLA7nlsPdyQFvP9gbcjkPzxARWYtWv5rGZDLB398fS5cuRb9+/TB69Gi88sorWLJkSZPrJCcno6KiouGRm5vb2jHJih27VIH3d9VfPTP77kgEqp0FJyIiInOYdQKrr68vFAoFCgsLG40XFhaiXbt2V10nMDAQjo6OUCgUDWPdu3dHQUEB9Ho9lMorZ8VUqVRQqVTmRCM7pTMYkbThMOqMEoZHBuC+aF49Q0RkbczaM6JUKtGvXz/s2rWrYcxkMmHXrl2Ii4u76jqDBg1CVlYWTCZTw9jp06cRGBh41SJCZI75O0/jVGElfN2UmHdfL149Q0Rkhcw+TJOUlIRly5Zh9erVOHHiBJ588klotVokJiYCAMaNG4fk5OSG5Z988kmUlpbi2WefxenTp7F161bMmzcPU6ZMabnvguxS6vlSLN2dDQCYd18v+LhxbxoRkTUye56R0aNHo7i4GDNnzkRBQQH69OmD7du3N5zUmpOTA7n8j44TGhqKHTt2YNq0aejduzeCg4Px7LPP4qWXXmq574LsjlZnwL8/PwxJAh7oG4LbI69+mJCIiCyf2fOMiMB5RuivXt1yFGt+yUGQ2gnbpw2Bh9ONzWFDREStp1XmGSGyBD+dLsaaX3IAAO88FMUiQkRk5VhGyKpUVNfhxY2HAQCPDQzDoE6+ghMREdHfxTJCVmXWV5ko1OgQ4euKl+7oJjoOERG1AJYRshrfHs3HloxLkMuAd0dFwVmpuP5KRERk8VhGyCoUV+rw8uajAICn/tEJfdt7CU5EREQthWWELJ4kSUjedARl1XXoEeiBZ27rLDoSERG1IJYRsnifpebi+xNFUCrkmD86CkoH/tgSEdkS/lUni3amsBKzvjoGAEi6vQu6teM8M0REtoZlhCxWjd6IKWvTUVtnwuDOvnh8cIToSERE1ApYRshivf7NMZwurIKfuwrzR/WBXM6b4BER2SKWEbJIX2bkYd2BXMhkwPuj+8DPnTfBIyKyVSwjZHHOlWjx8qb6y3inDu2EgZxllYjIprGMkEXRGYyYui4dWr0RA8K9eRkvEZEdYBkhi5Ky7SQy8zTwcnHEBw9Hw0HBH1EiIlvHv/RkMXYcK8Cqn88DAOaP6oN2aiexgYiIqE2wjJBFuFhWjRc+r78b7+NDIjC0m7/gRERE1FZYRki4OqMJU9cdgqbWgD6hnnj+9q6iIxERURtiGSHh3vvuNA7llMPdyQH/90g0p3snIrIz/KtPQv14qghLfjoLAHjnwd4I9XYRnIiIiNoaywgJU6ipRdJn9eeJjIvrgDt6BgpOREREIrCMkBBGk4Rn1x9CqVaPHoEeeHlkd9GRiIhIEJYREuL//ncGv2SXwkWpwMIx0XByVIiOREREgrCMUJv7+WwJ3t91BgAw775eiPBzE5yIiIhEYhmhNlVSpcNz6zMgScComBDcGx0sOhIREQnGMkJtps5owtS1h1BUqUNnfze8dnek6EhERGQBWEaoTUiShJlfZmJ/9mW4KhVYNLYvXJQOomMREZEFYBmhNrFi33msO5ALuQz4vzHR6BLgLjoSERFZCJYRanU/nCzCG1uPAwBeHtkdt3YLEJyIiIgsCcsItapTBZWYuu4QTBLwcP9QTLw5XHQkIiKyMCwj1GpKqnSYuPogqnQG3BThjdfv6QmZTCY6FhERWRiWEWoVOoMRT3yShotlNQjzccGHY/vxBnhERHRVfHegFidJEpI3HUXqhTK4Ozngo/H94eWqFB2LiIgsFMsItbglP2VjU3oeFHIZFo/ti07+nGGViIiaxjJCLWrHsQK8veMkAOC1hB4Y3NlPcCIiIrJ0LCPUYjLzKhqmeh8X1wGPxoWJjkRERFbghsrIokWLEBYWBicnJ8TGxuLAgQPNWm/9+vWQyWS49957b2SzZMGKNLWY/HEqauqMGNzZFzPv6iE6EhERWQmzy8iGDRuQlJSEWbNmIT09HVFRURg+fDiKioquud758+fx/PPPY/DgwTcclixTbZ0Rkz9JQ35FLSL8XLFwTF84KLjTjYiImsfsd4z58+dj8uTJSExMRI8ePbBkyRK4uLhgxYoVTa5jNBoxduxYzJ49GxEREX8rMFkWSZLwwsYjOJxbDk8XR6wY3x9qZ0fRsYiIyIqYVUb0ej3S0tIQHx//xxeQyxEfH4/9+/c3ud7rr78Of39/TJw4sVnb0el00Gg0jR5kmT7YlYWvD1+Cg1yGD8f2Q5ivq+hIRERkZcwqIyUlJTAajQgIaHxvkYCAABQUFFx1nb1792L58uVYtmxZs7eTkpICtVrd8AgNDTUnJrWRb45cwn++Pw0AmHtvT8R19BGciIiIrFGrHtivrKzEo48+imXLlsHX17fZ6yUnJ6OioqLhkZub24op6UYczi3Hvz87DACYdHM4Hh7QXnAiIiKyVg7mLOzr6wuFQoHCwsJG44WFhWjXrt0Vy589exbnz59HQkJCw5jJZKrfsIMDTp06hY4dO16xnkqlgkqlMicataH8ihpM/jgVOoMJt3bzR/LI7qIjERGRFTNrz4hSqUS/fv2wa9euhjGTyYRdu3YhLi7uiuW7deuGo0ePIiMjo+Fx9913Y+jQocjIyODhFytUrTdg0upUFFXq0DXAHe8/3AcKOW9+R0REN86sPSMAkJSUhPHjxyMmJgYDBgzAggULoNVqkZiYCAAYN24cgoODkZKSAicnJ/Ts2bPR+p6engBwxThZvto6I55ck45jlzTwcVXio/ExcHfilTNERPT3mF1GRo8ejeLiYsycORMFBQXo06cPtm/f3nBSa05ODuRyzjFha2rrjJj8cSr2nCmBk6Mc/320H0K9XUTHIiIiGyCTJEkSHeJ6NBoN1Go1Kioq4OHhITqO3flzEXF2VGDFY/155QwREV1Xc9+/zd4zQvalRl9fRPZmlcBFqcDKx/ojNoJFhIiIWg7LCDWpRm/ExNUH8fPZy3BVKrAycQAGhHuLjkVERDaGZYSuqlpvwMRVqdifXV9EVk8YgJgwFhEiImp5LCN0hWq9AYkrD+LXc6VwUzlg9YT+6NeBRYSIiFoHywg1otUZkLjqIA6cK4W7ygGrJw5A3/ZeomMREZENYxmhBlU6AxJXHsDB82VwVzng44kDEM0iQkRErYxlhADUF5HHVhxA6oUyuDs54JOJsegT6ik6FhER2QGWEUJlbR0eW3kQaRfK4OHkgDWTYtE7xFN0LCIishMsI3ZOU1uH8SsO4FBOOdTOjlgzMRa9QtSiYxERkR1hGbFjmto6jFt+ABm59UXk00mx6BnMIkJERG2LZcROVdTUYdyKAzicWw5Pl/o9IiwiREQkAsuIHaqorsOjK37FkYsV8HJxxKeTbkKPIN7zh4iIxGAZsTMV1XX45/JfcTSvAt6uSnw6KRbdA1lEiIhIHJYRO1Jercc/l/+KzDwNvF2VWDs5Ft3asYgQEZFYLCN2okyrx9iPfsXxfA18XJVYO/kmdG3nLjoWERERy4g9KP2tiJzI18DXrb6IdAlgESEiIsvAMmLjSrV6jFn2C04WVMLXTYV1k2PRmUWEiIgsCMuIDcsrr8HEVQdxsqASfu4qrJt8Ezr5u4mORURE1AjLiI367lgBXth4BBU1dfB3V2Hd4zehox+LCBERWR6WERujN5iQ8u0JrNx3HgAQFaLGwjF9EertIjYYERFRE1hGbEjO5Wo8vS4dRy5WAAAm3RyOF+/oBqWDXHAyIiKiprGM2IhtR/Px0sYjqNQZ4OniiHcfjEJ8jwDRsYiIiK6LZcTK1dYZMXfrcaz5JQcAENPBCx88Eo0gT2fByYiIiJqHZcSKZRdXYcraQziRrwEAPPWPjpg2rAscFTwsQ0RE1oNlxEptOZSHlzcfRbXeCB9XJeaP7oNbuviJjkVERGQ2lhErU6M34rWvjmFDai4A4KYIb7z/cDQCPJwEJyMiIroxLCNW5HRhJaZ8mo4zRVWQyYBnbu2MZ27rDIVcJjoaERHRDWMZsQKSJOHztIuY+WUmautM8HNX4f3RfTCwk6/oaERERH8by4iFq9IZMGNLJjYfygMADO7si/+M7gNfN5XgZERERC2DZcSCHb+kwdNr05FdooVCLkPSsC548paOkPOwDBER2RCWEQskSRI+/TUHr39zHHqDCYFqJ3zwSDT6h3mLjkZERNTiWEYsjKa2DsmbjmLrkXwAwG3d/PHuQ1HwclUKTkZERNQ6WEYsyJGL5Xh67SHklFbDQS7D9BHdMPHmcMhkPCxDRES2i2XEAkiShJX7ziPl2xOoM0oI9nTGwjHRiG7vJToaERFRq2MZEay8Wo8XNh7BzuOFAIA7ItvhrQd6Q+3iKDgZERFR27ihm5gsWrQIYWFhcHJyQmxsLA4cONDkssuWLcPgwYPh5eUFLy8vxMfHX3N5e5J2oQx3frAXO48XQqmQY/bdkfjwn31ZRIiIyK6YXUY2bNiApKQkzJo1C+np6YiKisLw4cNRVFR01eV//PFHPPLII/jhhx+wf/9+hIaG4vbbb0deXt7fDm+tTCYJS346i1H/3Y+88hp08HHBpqcGYvzAMJ4fQkREdkcmSZJkzgqxsbHo378/Fi5cCAAwmUwIDQ3F1KlTMX369OuubzQa4eXlhYULF2LcuHHN2qZGo4FarUZFRQU8PDzMiWtxLlfp8O/PD+PHU8UAgISoIMy7ryfcnbg3hIiIbEtz37/NOmdEr9cjLS0NycnJDWNyuRzx8fHYv39/s75GdXU16urq4O3d9JwZOp0OOp2u4blGozEnpsX6Nfsynll/CIUaHVQOcrx2dyQe7h/KvSFERGTXzCojJSUlMBqNCAgIaDQeEBCAkydPNutrvPTSSwgKCkJ8fHyTy6SkpGD27NnmRLNoh3PLsWxPNrYdzYdJAjr6uWLR2L7o1s669/IQERG1hDa9mubNN9/E+vXr8eOPP8LJqelb3icnJyMpKanhuUajQWhoaFtEbDEmk4T/nSzC0j3ZOHCutGH8gb4heP2eSLiqeCETERERYGYZ8fX1hUKhQGFhYaPxwsJCtGvX7prrvvvuu3jzzTfx/fffo3fv3tdcVqVSQaWyzhvB1dYZsSk9Dx/tzUZ2sRYA4CCX4e4+QZh0cwR6BHFvCBER0Z+ZVUaUSiX69euHXbt24d577wVQfwLrrl278PTTTze53ttvv4033ngDO3bsQExMzN8KbKlKtXp8sv8CPt5/Hpe1egCAu5MDxsS2x2MDwxCodhackIiIyDKZfawgKSkJ48ePR0xMDAYMGIAFCxZAq9UiMTERADBu3DgEBwcjJSUFAPDWW29h5syZWLt2LcLCwlBQUAAAcHNzg5ubWwt+K2JkF1dh+d5z2Jh2ETqDCQAQ7OmMCTeHY3T/ULjxcAwREdE1mf1OOXr0aBQXF2PmzJkoKChAnz59sH379oaTWnNyciCX/zF9yYcffgi9Xo8HH3yw0deZNWsWXnvttb+XXhBJkpB6oQzLdmdj54lC/H5xdK9gNR4fEoERPdvBQXFD88kRERHZHbPnGRHBUuYZMZok7DhWgKW7s5GRW94wfls3f0weEoHYcG9epktERPSbVplnxF5pdQZ8npqL5fvOIbe0BgCgdJDjgb7BmHhzBDr5W//hJiIiIlFYRq6hSFOLVT+fx6e/5qCipg4A4OXiiEfjwvDoTR3g526dV/wQERFZEpaRqzhVUImP9mTjy4xL0BvrT0oN83HBxMEReLBvCJyVCsEJiYiIbAfLyG8kScLPZy9j6e5s/HS6uGE8poMXJg+JQHz3ACjkPB+EiIiopdl9GakzmvDNkUtYtvscjufX3wNHLgPu6NkOkwZHoG97L8EJiYiIbJvdlhFNbR3WH8jByn3nkV9RCwBwdlRgVEwIJtwcjg4+roITEhER2Qe7KyN55TVYufcc1h/MRZXOAADwdVMhcVAYxsa2h6eLUnBCIiIi+2I3ZSQzrwJLd2dj69F8GE31U6t09nfD5CERuKdPEFQOPCmViIhIBJsuIyaThJ9OF2Pp7mzsz77cMD6okw8mDY7AP7r4cZIyIiIiwWyyjNTWGfFlRh6W7TmHrKIqAIBCLkNC70BMGhyBnsFqwQmJiIjodzZVRsq0eqz55QJW77+AkiodAMBN9cedc4M8eedcIiIiS2MTZeTCZS2W7z2Hz1JzUVtXP0lZkNqp4c657k6OghMSERFRU6y6jKT9dufcHccLGu6cGxnkgceHRGBkr0A48s65REREFs/qyojRJGHn8fo756bnlDeMD+3qh8lDIhAX4cOTUomIiKyIVZWR9Qcu4NNDJbhwuRoAoFTIcV90MCYNDkfnAHfB6YiIiOhGWFUZmbv1JOQqF3i6OOKfsR0wbmAH+Ls7iY5FREREf4NVlZEQL2c8MSwSD/YLgYvSqqITERFRE6zqHX3rM4Ph5ck5QoiIiGyJVV1uopDzxFQiIiJbY1VlhIiIiGwPywgREREJxTJCREREQrGMEBERkVAsI0RERCQUywgREREJxTJCREREQrGMEBERkVAsI0RERCQUywgREREJxTJCREREQrGMEBERkVAsI0RERCSUg+gAzSFJEgBAo9EITkJERETN9fv79u/v402xijJSWVkJAAgNDRWchIiIiMxVWVkJtVrd5Odl0vXqigUwmUy4dOkS3N3dIZPJRMe5YRqNBqGhocjNzYWHh4foOBaHr0/T+NpcG1+fa+Prc218fa7t77w+kiShsrISQUFBkMubPjPEKvaMyOVyhISEiI7RYjw8PPgDfw18fZrG1+ba+PpcG1+fa+Prc203+vpca4/I73gCKxEREQnFMkJERERCsYy0IZVKhVmzZkGlUomOYpH4+jSNr8218fW5Nr4+18bX59ra4vWxihNYiYiIyHZxzwgREREJxTJCREREQrGMEBERkVAsI0RERCQUy0gb+PDDD9G7d++GCWPi4uLw7bffio5lkd58803IZDI899xzoqNYhNdeew0ymazRo1u3bqJjWZS8vDz885//hI+PD5ydndGrVy+kpqaKjmURwsLCrvj5kclkmDJliuhowhmNRsyYMQPh4eFwdnZGx44dMWfOnOveQ8WeVFZW4rnnnkOHDh3g7OyMgQMH4uDBg62yLauYgdXahYSE4M0330Tnzp0hSRJWr16Ne+65B4cOHUJkZKToeBbj4MGD+O9//4vevXuLjmJRIiMj8f333zc8d3Dgr+3vysrKMGjQIAwdOhTffvst/Pz8cObMGXh5eYmOZhEOHjwIo9HY8DwzMxPDhg3DQw89JDCVZXjrrbfw4YcfYvXq1YiMjERqaioSExOhVqvxzDPPiI5nESZNmoTMzEx88sknCAoKwpo1axAfH4/jx48jODi4RbfFS3sF8fb2xjvvvIOJEyeKjmIRqqqq0LdvXyxevBhz585Fnz59sGDBAtGxhHvttdewZcsWZGRkiI5ikaZPn459+/Zhz549oqNYheeeew7ffPMNzpw5Y9X3+WoJd911FwICArB8+fKGsQceeADOzs5Ys2aNwGSWoaamBu7u7vjyyy9x5513Noz369cPI0aMwNy5c1t0ezxM08aMRiPWr18PrVaLuLg40XEsxpQpU3DnnXciPj5edBSLc+bMGQQFBSEiIgJjx45FTk6O6EgW46uvvkJMTAweeugh+Pv7Izo6GsuWLRMdyyLp9XqsWbMGEyZMsPsiAgADBw7Erl27cPr0aQDA4cOHsXfvXowYMUJwMstgMBhgNBrh5OTUaNzZ2Rl79+5t8e1xf28bOXr0KOLi4lBbWws3Nzds3rwZPXr0EB3LIqxfvx7p6emtdizSmsXGxmLVqlXo2rUr8vPzMXv2bAwePBiZmZlwd3cXHU+47OxsfPjhh0hKSsLLL7+MgwcP4plnnoFSqcT48eNFx7MoW7ZsQXl5OR577DHRUSzC9OnTodFo0K1bNygUChiNRrzxxhsYO3as6GgWwd3dHXFxcZgzZw66d++OgIAArFu3Dvv370enTp1afoMStQmdTiedOXNGSk1NlaZPny75+vpKx44dEx1LuJycHMnf3186fPhww9gtt9wiPfvss+JCWbCysjLJw8ND+uijj0RHsQiOjo5SXFxco7GpU6dKN910k6BEluv222+X7rrrLtExLMa6deukkJAQad26ddKRI0ekjz/+WPL29pZWrVolOprFyMrKkoYMGSIBkBQKhdS/f39p7NixUrdu3Vp8Wywjgtx2223S448/LjqGcJs3b274Qf/9AUCSyWSSQqGQDAaD6IgWJyYmRpo+fbroGBahffv20sSJExuNLV68WAoKChKUyDKdP39eksvl0pYtW0RHsRghISHSwoULG43NmTNH6tq1q6BElquqqkq6dOmSJEmSNGrUKGnkyJEtvg2eMyKIyWSCTqcTHUO42267DUePHkVGRkbDIyYmBmPHjkVGRgYUCoXoiBalqqoKZ8+eRWBgoOgoFmHQoEE4depUo7HTp0+jQ4cOghJZppUrV8Lf37/RiYj2rrq6GnJ547dAhUIBk8kkKJHlcnV1RWBgIMrKyrBjxw7cc889Lb4NnjPSBpKTkzFixAi0b98elZWVWLt2LX788Ufs2LFDdDTh3N3d0bNnz0Zjrq6u8PHxuWLcHj3//PNISEhAhw4dcOnSJcyaNQsKhQKPPPKI6GgWYdq0aRg4cCDmzZuHUaNG4cCBA1i6dCmWLl0qOprFMJlMWLlyJcaPH8/Lwv8kISEBb7zxBtq3b4/IyEgcOnQI8+fPx4QJE0RHsxg7duyAJEno2rUrsrKy8MILL6Bbt25ITExs+Y21+L4WusKECROkDh06SEqlUvLz85Nuu+026bvvvhMdy2LxnJE/jB49WgoMDJSUSqUUHBwsjR49WsrKyhIdy6J8/fXXUs+ePSWVSiV169ZNWrp0qehIFmXHjh0SAOnUqVOio1gUjUYjPfvss1L79u0lJycnKSIiQnrllVcknU4nOprF2LBhgxQRESEplUqpXbt20pQpU6Ty8vJW2RbnGSEiIiKheM4IERERCcUyQkREREKxjBAREZFQLCNEREQkFMsIERERCcUyQkREREKxjBAREZFQLCNEREQkFMsIERERCcUyQkREREKxjBAREZFQLCNEREQk1P8Dy3EjoiTKkUIAAAAASUVORK5CYII=","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["f0 = 1000\n","fc = 0.1*f0\n","freqs = np.linspace(0, 10*f0, N)\n","# Filtre 1 : passe bas d'ordre 1 avec fc=0.1*f0\n","def H(f):\n","    return 1/(1+1j*(f/fc))\n","def G(f):\n","    return (20*np.log(np.abs(H(f))))\n","def phi(f):\n","    return -np.angle(H(f))\n","\n","plt.clf()\n","plt.plot(np.log(freqs), G(freqs))\n","plt.show()\n","plt.plot(np.log(freqs), phi(freqs))\n","plt.show()"]},{"cell_type":"markdown","metadata":{},"source":["8. Reproduire la sorties des filtres passe-bas d'ordre 2 en utilisant la même méthode.<br>\n","Pour les plus motivés, reproduire également la sortie d'un filtre passe-bande sur l'harmonique 5.\n"]},{"cell_type":"code","execution_count":10,"metadata":{"trusted":true},"outputs":[{"name":"stderr","output_type":"stream","text":["/var/folders/f3/68h644h17rzcj7c0b9062v240000gn/T/ipykernel_3623/2507783765.py:13: RuntimeWarning: divide by zero encountered in log\n","  plt.plot(np.log(freqs), G2(freqs))\n"]},{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"},{"name":"stderr","output_type":"stream","text":["/var/folders/f3/68h644h17rzcj7c0b9062v240000gn/T/ipykernel_3623/2507783765.py:15: RuntimeWarning: divide by zero encountered in log\n","  plt.plot(np.log(freqs), phi2(freqs))\n"]},{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["# Filtre 2 : passe bas d'ordre 2 avec fc=0.4*f0\n","#Fonction de transfert d'un filtre d'ordre 2 : \n","fc = 0.4*f0\n","Q = 3\n","def H2(f):\n","    return 1/(1+1j*(f/fc)/Q-(f/fc)**2)\n","def G2(f):\n","    return (20*np.log(np.abs(H2(f))))\n","def phi2(f):\n","    return -np.angle(H2(f))\n","\n","plt.clf()\n","plt.plot(np.log(freqs), G2(freqs))\n","plt.show()\n","plt.plot(np.log(freqs), phi2(freqs))\n","plt.show()\n","# Code à remplir"]},{"cell_type":"code","execution_count":null,"metadata":{"vscode":{"languageId":"html"}},"outputs":[],"source":["<div style=\"page-break-after: always;\"></div>"]},{"cell_type":"markdown","metadata":{},"source":["---\n","\n","## Filtrage numérique en appliquant une relation de récurrence\n","\n","---\n","\n","9. Reproduire à nouveau l'effet du filtre passe-bas sur le signal créneau, sachant que la fonction de transfert analogique d'un filtre passe-bas du premier ordre est :\n","$$\n","\\underline{H}(j\\omega) = \\frac{1}{1 + j\\dfrac{\\omega}{\\omega_c}} = \\frac{\\underline{s}(t)}{\\underline{e}(t)}\n","$$\n","où $\\omega_c$ est la pulsation de coupure. Lorsqu'on repasse dans le domaine temporel, cela correspond à l'équation différentielle :\n","$$\n","\\boxed{\\underline{e}(t) = \\underline{s}(t) + \\frac{1}{\\omega_c}\\, j\\omega\\, \\underline{s}(t) \\hspace{0.2cm} \\Longrightarrow \\hspace{0.2cm} \\frac{1}{\\omega_c}\\, \\frac{ds}{dt} + s = e(t)}\n","$$\n","\n","> Pour des données numériques échantillonnées avec une période $T_e$, l'idée est de remplacer la dérivée temporelle $\\dot{s}$ par le taux d'accroissement :\n","$$\n","\\frac{ds}{dt}(t) \\hspace{0.2cm} \\longleftrightarrow \\hspace{0.2cm} \\frac{s_n - s_{n-1}}{T_e}\n","$$\n","> ce qui permet de transformer l'équation différentielle en :\n","$$\n","\\boxed{\\frac{1}{\\omega_c} \\, \\frac{s_n - s_{n-1}}{T_e} + s_n = e_n \\hspace{0.2cm} \\Longleftrightarrow \\hspace{0.2cm} s_n = \\frac{s_{n-1}}{1 + \\omega_cT_e} + \\frac{\\omega_cT_e}{1 + \\omega_cT_e}\\, e_n}\n","$$\n","\n","Les $\\{e_n\\}$, $T_e$ étant connus, on choisit la pulsation de coupure $\\omega_c$ souhaitée : les différents échantillons $\\{s_n\\}$ se calculent ensuite à l'aide de la récurrence ci-dessus avec une condition initiale pour $s_0$. On a donc remplacé une équation différentielle par une relation de récurrence."]},{"cell_type":"code","execution_count":11,"metadata":{"trusted":true},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["# Code fourni\n","# Filtre 1 : passe bas d'ordre 1 avec fc=0.1*f0\n","s0 = 0\n","N = 1000\n","tmin = 0\n","tmax = 5e-3\n","times = np.linspace(tmin, tmax, N)\n","e = crenau(times, 250)\n","\n","def s(s0, e):\n","    wc = 2*np.pi*fc\n","    Te = (tmax-tmin)/N\n","    s = np.zeros(N)\n","    s[0] = s0\n","    for n in range(1, N):\n","        s[n] = s[n-1]/(1+wc*Te) + e[n]*wc*Te/(1+wc*Te)\n","    return s \n","\n","s1 = s(s0, e)\n","\n","plt.plot(times, e)\n","plt.plot(times, s1)\n","plt.show()"]},{"cell_type":"markdown","metadata":{},"source":["9. Reproduire les courbes pour les filtres en utilisant la même méthode de la récurrence."]},{"cell_type":"code","execution_count":12,"metadata":{"trusted":true},"outputs":[],"source":["# Filtre 2 : passe pas d'ordre 2\n","s0 = 0\n","N = 1000\n","tmin = 0\n","tmax = 5e-3\n","times = np.linspace(tmin, tmax, N)\n","e = crenau(times, 250)\n","\n","# Code à remplir par l'élève."]}],"metadata":{"kernelspec":{"display_name":"Python 3","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":"3.11.2"},"toc":{"base_numbering":1,"nav_menu":{},"number_sections":true,"sideBar":true,"skip_h1_title":true,"title_cell":"Table des matières","title_sidebar":"Contents","toc_cell":true,"toc_position":{"height":"calc(100% - 180px)","left":"10px","top":"150px","width":"165px"},"toc_section_display":false,"toc_window_display":false}},"nbformat":4,"nbformat_minor":2}