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TP Traitement du Signal (Octave, complet)
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "# Traitement du Signal: TP d'Initiation\n", | |
| "\n", | |
| "## Exercice 1" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "n = -128:128;\n", | |
| "u = n > 0;\n", | |
| "x = (1/2) .^ n .* u;\n", | |
| "f = linspace(-1/2, 1/2, length(x));\n", | |
| "X = fftshift(fft(x));" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<IPython.core.display.Image object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plot(n, x)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<IPython.core.display.Image object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plot(f, abs(X))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "2) Le filtre est de type passe-bas, car un signal de fréquence (normalisée) 0 sera laissé tel-quel, alors qu'un signal de fréquence 0.5 sera atténué." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<IPython.core.display.Image object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "f_c = 1/4;\n", | |
| "pb = f > -0.25 & f < 0.25;\n", | |
| "plot(f, pb);" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "f_1 = 1/5;\n", | |
| "f_2 = 1/3;\n", | |
| "f_3 = 2/5;\n", | |
| "y = cos(2 * pi * f_1 * n) + cos(2 * pi * f_2 * n) + cos(2 * pi * f_3 * n);" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 6, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<IPython.core.display.Image object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plot(n, y)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "2) Le signal est échantilloné avec une fréquence de 1.\n", | |
| "\n", | |
| "3) Un filtre passe-bas de fréquence de coupure entre $ f_1 $ et $ f_2 $ permettrait de filtrer $ f_2 $ et $ f_3 $ sans toucher à $ f_1 $. Une fréquence de $ \\frac{1}{4} $ conviendrait, par exemple." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 7, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<IPython.core.display.Image object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "ph = f > -0.25 & f < 0.25;\n", | |
| "Y = fftshift(fft(y));\n", | |
| "Y2 = Y .* ph;\n", | |
| "y2 = real(ifft(ifftshift(Y2)));\n", | |
| "\n", | |
| "subplot(2, 1, 1)\n", | |
| "plot(n, y2)\n", | |
| "title(\"Signal\")\n", | |
| "subplot(2, 1, 2)\n", | |
| "plot(f, abs(Y2))\n", | |
| "title(\"FFT\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "5) Pour modifier le filtrage, il faut décaler la fréquence de coupure pour qu'elle soit en dessous de $ f_1 $. Par exemple, $ f_c = 0.1 $ conviendrait." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 8, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<IPython.core.display.Image object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "ph = f > -0.1 & f < 0.1;\n", | |
| "Y3 = ph .* Y;\n", | |
| "y3 = real(ifft(ifftshift(Y3)));\n", | |
| "\n", | |
| "subplot(2, 1, 1)\n", | |
| "plot(n, y3)\n", | |
| "title(\"Signal\")\n", | |
| "\n", | |
| "subplot(2, 1, 2)\n", | |
| "plot(f, abs(Y3))\n", | |
| "title(\"FFT\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Exercice 2" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 9, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<IPython.core.display.Image object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "Fe = 10000;\n", | |
| "F0 = 3000;\n", | |
| "t = 0:1/Fe:0.01;\n", | |
| "fftt = linspace(-Fe/2, Fe/2, length(t));\n", | |
| "ye = cos(2*pi*F0*t);\n", | |
| "Ye = fftshift(fft(ye));\n", | |
| "\n", | |
| "subplot(3, 1, 1)\n", | |
| "plot(t, ye)\n", | |
| "title(\"Signal\")\n", | |
| "\n", | |
| "subplot(3, 1, 2)\n", | |
| "plot(fftt, abs(Ye))\n", | |
| "title(\"FFT\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 10, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<IPython.core.display.Image object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# 2)\n", | |
| "Fe = 4000;\n", | |
| "F0 = 3000;\n", | |
| "t = 0:1/Fe:0.01;\n", | |
| "fftt = linspace(-Fe/2, Fe/2, length(t));\n", | |
| "ye = cos(2*pi*F0*t);\n", | |
| "Ye = fftshift(fft(ye));\n", | |
| "\n", | |
| "subplot(2, 1, 1)\n", | |
| "plot(t, ye)\n", | |
| "title(\"Signal\")\n", | |
| "\n", | |
| "subplot(2, 1, 2)\n", | |
| "plot(fftt, abs(Ye))\n", | |
| "title(\"FFT\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "3) La transformée de Fourier du second signal est incorrect, car le signal est sous-échantilloné dans le deuxième cas; il ne respecte pas le théorème de Shannon." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "L'instruction `load` charge un fichier binaire représentant des données matricielles. La fonction `sound` permet d'écouter les données audio représentées par la matrice passée en arguements." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 11, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Fe = 8192\n", | |
| "Expression 'alsa_snd_pcm_hw_params_set_buffer_size_near( pcm, hwParams, &alsaBufferFrames )' failed in 'src/hostapi/alsa/pa_linux_alsa.c', line: 923\n", | |
| "Expression 'alsa_snd_pcm_hw_params_set_buffer_size_near( pcm, hwParams, &alsaBufferFrames )' failed in 'src/hostapi/alsa/pa_linux_alsa.c', line: 923\n", | |
| "Expression 'alsa_snd_pcm_hw_params_set_buffer_size_near( pcm, hwParams, &alsaBufferFrames )' failed in 'src/hostapi/alsa/pa_linux_alsa.c', line: 923\n", | |
| "Expression 'alsa_snd_pcm_hw_params_set_buffer_size_near( pcm, hwParams, &alsaBufferFrames )' failed in 'src/hostapi/alsa/pa_linux_alsa.c', line: 923\n", | |
| "Expression 'alsa_snd_pcm_hw_params_set_buffer_size_near( pcm, hwParams, &alsaBufferFrames )' failed in 'src/hostapi/alsa/pa_linux_alsa.c', line: 923\n", | |
| "Expression 'alsa_snd_pcm_hw_params_set_buffer_size_near( pcm, hwParams, &alsaBufferFrames )' failed in 'src/hostapi/alsa/pa_linux_alsa.c', line: 923\n", | |
| "ALSA lib confmisc.c:767:(parse_card) cannot find card '0'\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_card_driver returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:392:(snd_func_concat) error evaluating strings\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_concat returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:1246:(snd_func_refer) error evaluating name\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_refer returned error: No such file or directory\n", | |
| "ALSA lib conf.c:5231:(snd_config_expand) Evaluate error: No such file or directory\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM sysdefault\n", | |
| "ALSA lib confmisc.c:767:(parse_card) cannot find card '0'\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_card_driver returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:392:(snd_func_concat) error evaluating strings\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_concat returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:1246:(snd_func_refer) error evaluating name\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_refer returned error: No such file or directory\n", | |
| "ALSA lib conf.c:5231:(snd_config_expand) Evaluate error: No such file or directory\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM sysdefault\n", | |
| "ALSA lib confmisc.c:767:(parse_card) cannot find card '0'\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_card_driver returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:392:(snd_func_concat) error evaluating strings\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_concat returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:1246:(snd_func_refer) error evaluating name\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_refer returned error: No such file or directory\n", | |
| "ALSA lib conf.c:5231:(snd_config_expand) Evaluate error: No such file or directory\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM front\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM cards.pcm.rear\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM cards.pcm.center_lfe\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM cards.pcm.side\n", | |
| "ALSA lib confmisc.c:767:(parse_card) cannot find card '0'\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_card_driver returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:392:(snd_func_concat) error evaluating strings\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_concat returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:1246:(snd_func_refer) error evaluating name\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_refer returned error: No such file or directory\n", | |
| "ALSA lib conf.c:5231:(snd_config_expand) Evaluate error: No such file or directory\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM surround21\n", | |
| "ALSA lib confmisc.c:767:(parse_card) cannot find card '0'\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_card_driver returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:392:(snd_func_concat) error evaluating strings\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_concat returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:1246:(snd_func_refer) error evaluating name\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_refer returned error: No such file or directory\n", | |
| "ALSA lib conf.c:5231:(snd_config_expand) Evaluate error: No such file or directory\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM surround21\n", | |
| "ALSA lib confmisc.c:767:(parse_card) cannot find card '0'\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_card_driver returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:392:(snd_func_concat) error evaluating strings\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_concat returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:1246:(snd_func_refer) error evaluating name\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_refer returned error: No such file or directory\n", | |
| "ALSA lib conf.c:5231:(snd_config_expand) Evaluate error: No such file or directory\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM surround40\n", | |
| "ALSA lib confmisc.c:767:(parse_card) cannot find card '0'\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_card_driver returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:392:(snd_func_concat) error evaluating strings\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_concat returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:1246:(snd_func_refer) error evaluating name\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_refer returned error: No such file or directory\n", | |
| "ALSA lib conf.c:5231:(snd_config_expand) Evaluate error: No such file or directory\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM surround41\n", | |
| "ALSA lib confmisc.c:767:(parse_card) cannot find card '0'\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_card_driver returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:392:(snd_func_concat) error evaluating strings\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_concat returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:1246:(snd_func_refer) error evaluating name\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_refer returned error: No such file or directory\n", | |
| "ALSA lib conf.c:5231:(snd_config_expand) Evaluate error: No such file or directory\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM surround50\n", | |
| "ALSA lib confmisc.c:767:(parse_card) cannot find card '0'\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_card_driver returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:392:(snd_func_concat) error evaluating strings\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_concat returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:1246:(snd_func_refer) error evaluating name\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_refer returned error: No such file or directory\n", | |
| "ALSA lib conf.c:5231:(snd_config_expand) Evaluate error: No such file or directory\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM surround51\n", | |
| "ALSA lib confmisc.c:767:(parse_card) cannot find card '0'\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_card_driver returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:392:(snd_func_concat) error evaluating strings\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_concat returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:1246:(snd_func_refer) error evaluating name\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_refer returned error: No such file or directory\n", | |
| "ALSA lib conf.c:5231:(snd_config_expand) Evaluate error: No such file or directory\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM surround71\n", | |
| "ALSA lib confmisc.c:767:(parse_card) cannot find card '0'\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_card_driver returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:392:(snd_func_concat) error evaluating strings\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_concat returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:1246:(snd_func_refer) error evaluating name\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_refer returned error: No such file or directory\n", | |
| "ALSA lib conf.c:5231:(snd_config_expand) Evaluate error: No such file or directory\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM iec958\n", | |
| "ALSA lib confmisc.c:767:(parse_card) cannot find card '0'\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_card_driver returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:392:(snd_func_concat) error evaluating strings\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_concat returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:1246:(snd_func_refer) error evaluating name\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_refer returned error: No such file or directory\n", | |
| "ALSA lib conf.c:5231:(snd_config_expand) Evaluate error: No such file or directory\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM spdif\n", | |
| "ALSA lib confmisc.c:767:(parse_card) cannot find card '0'\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_card_driver returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:392:(snd_func_concat) error evaluating strings\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_concat returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:1246:(snd_func_refer) error evaluating name\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_refer returned error: No such file or directory\n", | |
| "ALSA lib conf.c:5231:(snd_config_expand) Evaluate error: No such file or directory\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM spdif\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM cards.pcm.hdmi\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM cards.pcm.hdmi\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM cards.pcm.modem\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM cards.pcm.modem\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM cards.pcm.phoneline\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM cards.pcm.phoneline\n", | |
| "ALSA lib pcm_hw.c:1829:(_snd_pcm_hw_open) Invalid value for card\n", | |
| "ALSA lib pcm_hw.c:1829:(_snd_pcm_hw_open) Invalid value for card\n", | |
| "ALSA lib pcm_hw.c:1829:(_snd_pcm_hw_open) Invalid value for card\n", | |
| "ALSA lib pcm_hw.c:1829:(_snd_pcm_hw_open) Invalid value for card\n", | |
| "Cannot connect to server socket err = No such file or directory\n", | |
| "Cannot connect to server request channel\n", | |
| "jack server is not running or cannot be started\n", | |
| "JackShmReadWritePtr::~JackShmReadWritePtr - Init not done for -1, skipping unlock\n", | |
| "JackShmReadWritePtr::~JackShmReadWritePtr - Init not done for -1, skipping unlock\n", | |
| "Cannot connect to server socket err = No such file or directory\n", | |
| "Cannot connect to server request channel\n", | |
| "jack server is not running or cannot be started\n", | |
| "JackShmReadWritePtr::~JackShmReadWritePtr - Init not done for -1, skipping unlock\n", | |
| "JackShmReadWritePtr::~JackShmReadWritePtr - Init not done for -1, skipping unlock\n", | |
| "ALSA lib pcm_oss.c:377:(_snd_pcm_oss_open) Unknown field port\n", | |
| "ALSA lib pcm_oss.c:377:(_snd_pcm_oss_open) Unknown field port\n", | |
| "ALSA lib pcm_hw.c:1829:(_snd_pcm_hw_open) Invalid value for card\n", | |
| "ALSA lib pcm_hw.c:1829:(_snd_pcm_hw_open) Invalid value for card\n", | |
| "ALSA lib pcm_hw.c:1829:(_snd_pcm_hw_open) Invalid value for card\n", | |
| "ALSA lib pcm_hw.c:1829:(_snd_pcm_hw_open) Invalid value for card\n", | |
| "ALSA lib pcm_usb_stream.c:486:(_snd_pcm_usb_stream_open) Invalid type for card\n", | |
| "ALSA lib pcm_usb_stream.c:486:(_snd_pcm_usb_stream_open) Invalid type for card\n", | |
| "ALSA lib confmisc.c:767:(parse_card) cannot find card '0'\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_card_driver returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:392:(snd_func_concat) error evaluating strings\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_concat returned error: No such file or directory\n", | |
| "ALSA lib confmisc.c:1246:(snd_func_refer) error evaluating name\n", | |
| "ALSA lib conf.c:4743:(_snd_config_evaluate) function snd_func_refer returned error: No such file or directory\n", | |
| "ALSA lib conf.c:5231:(snd_config_expand) Evaluate error: No such file or directory\n", | |
| "ALSA lib pcm.c:2660:(snd_pcm_open_noupdate) Unknown PCM dmix\n", | |
| "Cannot connect to server socket err = No such file or directory\n", | |
| "Cannot connect to server request channel\n", | |
| "jack server is not running or cannot be started\n", | |
| "JackShmReadWritePtr::~JackShmReadWritePtr - Init not done for -1, skipping unlock\n", | |
| "JackShmReadWritePtr::~JackShmReadWritePtr - Init not done for -1, skipping unlock\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "load handel.mat;\n", | |
| "Fe = 8192\n", | |
| "\n", | |
| "sound(y, 2*Fe)\n", | |
| "sound(y, Fe/2)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "8) La lecture avec sur-échantillonage lit l'audio en accéléré et à une fréquence sonore plus haute, et inversement pour la lecture avec sous-échantillonage.\n", | |
| "\n", | |
| "## Exercice 3" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 12, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Fe = 44100\n", | |
| "freq = 261.63\n", | |
| "freq = 293.66\n", | |
| "freq = 329.63\n", | |
| "freq = 261.63\n", | |
| "freq = 329.63\n", | |
| "freq = 349.23\n", | |
| "freq = 392.00\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "function y = note(id, t)\n", | |
| " freq = 220 * 2 ^ ((3+id)/12)\n", | |
| " \n", | |
| " y = sin(2 * pi * freq * t);\n", | |
| "end\n", | |
| "\n", | |
| "Fe = 44100\n", | |
| "t = 0:1/Fe:0.2;\n", | |
| "tt = 0:1/Fe:0.4;\n", | |
| "frere_jacques = cat(2, note(0, t), note(2, t), note(4, t), note(0, t));\n", | |
| "dormez_vous = cat(2, note(4, t), note(5, t), note(7, tt));\n", | |
| "musique = cat(2, frere_jacques, frere_jacques, dormez_vous, dormez_vous);\n", | |
| "sound(musique * 0.1, Fe)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Exercice 4" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 13, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Fe = 8192\n", | |
| "len = 8.9249\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "load handel.mat;\n", | |
| "Fe = 8192\n", | |
| "y = transpose(y);\n", | |
| "len = length(y) / Fe" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "1) La longueur est de ~8.9 s" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 14, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<IPython.core.display.Image object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# 2)\n", | |
| "Y = fftshift(fft(y));\n", | |
| "X = linspace(-Fe/2, Fe/2, length(Y));\n", | |
| "plot(X, abs(Y))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 15, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<IPython.core.display.Image object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "t = (0:length(y)-1) ./ Fe;\n", | |
| "s = sin(2 * pi * 3000 * t)*0.5;\n", | |
| "plot(t, s);" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 16, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<IPython.core.display.Image object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "ys = y + s;\n", | |
| "plot(t, ys);" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 17, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<IPython.core.display.Image object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "YS = fftshift(fft(ys));\n", | |
| "X = linspace(-Fe/2, Fe/2, length(YS));\n", | |
| "\n", | |
| "plot(X, YS)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 18, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "sound(ys * 0.2, Fe)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 19, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<IPython.core.display.Image object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "f = (X < -3010) | (X > -2990) & (X < 2990) | (X > 3010);\n", | |
| "Y3 = -f .* YS;\n", | |
| "y3 = ifft(ifftshift(Y3));\n", | |
| "\n", | |
| "plot(t, y3)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "sound(y3, Fe)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# 9)\n", | |
| "REPETITIONS = 1000\n", | |
| "\n", | |
| "gauss = normrnd(0, 0.5, [REPETITIONS length(y)])" | |
| ] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "Octave", | |
| "language": "octave", | |
| "name": "octave" | |
| }, | |
| "language_info": { | |
| "file_extension": ".m", | |
| "help_links": [ | |
| { | |
| "text": "GNU Octave", | |
| "url": "https://www.gnu.org/software/octave/support.html" | |
| }, | |
| { | |
| "text": "Octave Kernel", | |
| "url": "https://github.com/Calysto/octave_kernel" | |
| }, | |
| { | |
| "text": "MetaKernel Magics", | |
| "url": "https://metakernel.readthedocs.io/en/latest/source/README.html" | |
| } | |
| ], | |
| "mimetype": "text/x-octave", | |
| "name": "octave", | |
| "version": "5.2.0" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 4 | |
| } |
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