{ "cells": [ { "cell_type": "markdown", "id": "c944a523", "metadata": {}, "source": [ "# Transformation de Fourier rapide\n", "\n", "On va illustrer le fonctionnement et l'utilité de la transformation de Fourier discrète par un exemple en traitement de signal acoustique. Les données dans le fichier \"trumpet.txt\" est l'amplitude en fonction du temps d'une onde sonore produite par une trompette. Elles ont été enrégistrées par un microphone, puis digitalisées avec un taux d'échantillonage de 44.1 kHz. On trace le signal pour $2^{16}=65536$ points de données, donc environ 1.5 s:" ] }, { "cell_type": "code", "execution_count": 1, "id": "544c33c6", "metadata": {}, "outputs": [ { "data": { "image/png": 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iNHbsWD3xxBOSzo5aRURE6OWXX9bIkSOVmZmp8PBwff755xo8eLAk6ciRI4qJidHChQvVp08fJSYmKjY2Vhs2bFDHjh0lSRs2bFDnzp21a9cutWzZUosWLdKAAQN06NAhRUVFSZLmzJmjYcOG6dixY5e9K7dUsbt4w300mrDA6hIAwGPcFRetV+5o59R9VuT726VGsi4lKSlJqamp6t27t2Obv7+/unfvrnXr1kmStm7dqoKCghJtoqKi1KZNG0eb9evXy263OwKWJHXq1El2u71EmzZt2jgCliT16dNHeXl52rp1a5n15eXlKSsrq8QDnuXj1futLgEAUIXcJmSlpp6dTBwREVFie0REhOO11NRU+fn5qXbt2pdsU7du3VL7r1u3bok2Fx6ndu3a8vPzc7S50NSpUx1zvOx2u2JiYirRS7iqvcey9eLCRKvLAABUIbcJWefYLlh5zDCMUtsudGGbstpXps35Jk6cqMzMTMfj0KFDl6wJ7mXvsVNWlwAAqGJuE7IiIyMlqdRI0rFjxxyjTpGRkcrPz1d6evol2xw9Wvrqr+PHj5doc+Fx0tPTVVBQUGqE6xx/f3+FhISUeMAz7DySpVFf/GR1GQCAKuY2Iatx48aKjIzU0qVLHdvy8/O1atUqdenSRZLUoUMH+fr6lmiTkpKi7du3O9p07txZmZmZ2rRpk6PNxo0blZmZWaLN9u3blZKS4mizZMkS+fv7q0OHDqb2E9VfcbGh4Z9tUaMJC9R+8hL1e3uN1SUBACzgY3UBFXHq1Cnt3fv7JfBJSUlKSEhQnTp11KBBA40dO1ZTpkxR8+bN1bx5c02ZMkVBQUEaMmSIJMlut+uBBx7QY489ptDQUNWpU0fjx49X27Zt1bNnT0lS69atdcstt2jEiBH68MMPJUkPPvigBgwYoJYtW0qSevfurdjYWA0dOlSvvvqqTp48qfHjx2vEiBGMUEFztxxyrIWVcbrA4moAwHPZZO3NC10qZG3ZskU33XST4/m4ceMkSffdd59mzpypxx9/XLm5uRo9erTS09PVsWNHLVmyRDVr1nS854033pCPj4/uuusu5ebmqkePHpo5c6a8vb0dbWbNmqUxY8Y4rkIcNGhQibW5vL29tWDBAo0ePVpdu3ZVYGCghgwZotdee83sHwGqqZW7j2nYp5v10E1N9e6KfVaXAwCoBlx2nSxXxzpZru1fWw7pmW+3K6+wWDe0CNfqPcetLgkAcIHBcTF6+Y6rnbrPinx/u9RIFlBdPP71L45/E7AAoHoyZO04kttMfAcAAKhOGMkCKiAzt0B7j2VfviEAwOMRsoByOnTytLq9ssLqMgAA5WT11YWcLgTK6bufj1hdAgDAhRCygHLKySu0ugQAgAshZAHlUFRs6L2VrH8FACg/QhZQDjPXHbC6BACAi2HiO3ARp/ML9ejcBDUKC9aHq/ZbXQ4AwMUQsoCLeGf5Xn2/46jVZQAAKslm7cWFnC4EypJ9poA5WACAK0LIAs5jGIa+2HBQbSctsboUAICLI2QB51n9a5qe/na71WUAANwAIQs4T9LxU1aXAABwEsPa+0MTsjxRYVGx5mxK1v7zAkVeYZGFFVUPh9NP6/Ule6wuAwDgJghZHmj2pmRN+Gabbn59lSTp71/9rJZPL9bBEzkWV2at619eoWxWdQcAt8HVhahyWw6ml3j+1dbDkqRP1iZZUU61sG5fmtUlAADcDOtkwaMlpeXoptdWWl0GAMANEbLgUQzDkGFIk/+7UzF1gvR//91pdUkAADdFyPJA519tsedotnWFVCHDMLTm1zQ9MjtevWIj9PX/TpECAGAWQpaHe/bf7r8m1NRFiSXuPUjAAgBUBUIWHGxWX4bhRMXFhk6ezteJU/nc3BkAPJTVX2uELLgNwzCUlVsoe5CvRn6xVUt3cnNnAIB1CFlwSYVFxZq1MVmdm4aqWXgNrd9/Qu+v3Ke1e1mKAQBQPRCyPND5dxk4fxK8YfX9ByrgmX9v1+xNhyRJsfVCtDMly+KKAAAoicVI4XL+uf6AI2BJImABAKolRrI8UGFRcZnbq/vEd8MwlFtQpKkLd1ldCgAAl0XI8kCLtqc6/n3hGcL3V+7Tyt3H9Nn91ynA17uKK7u04Z9t0bJdx6wuAwCAcuF0oYfbdOBkiecvL96ljUknNXfzoYu8wzoELACAKyFkoUxnCoqsLgEAAJdGyILDtt8yrS4BAAC3QciCw9aD6VaXAACA2yBkwSW89v1uq0sAAKBCCFkoU3VbzeGdFXutLgEA4HKs/TIjZKFMU6rRWlQnc/KtLgEAgAojZKHaG/n5FqtLAACgwliMFNVWxul8Df9si7YwIR8A4IIYyUK19e6KvQQsAIDLImSh2vp4TZLVJQAAUGmELAAA4JasvlKekIWLyskr1OT/7NSWC+5vWBX++8uRKj8mAADORMjCRb297Fd98mOS7vhgfZUeN+N0vh7+Mr5KjwkAcD+GYe3xCVm4qH3Hc6r8mAdP5Kj95KVVflwAAJyNkIVqIze/SN1fXWl1GQAAOAXrZOGisnILquxYJ07l6Y0f9lTZ8QAAMBshCxe1qYomvGfmFqjDCz9UybEAAJ6Dqwvh8XanZltdAgAATkfI8hA/7DyqlxfvUnGxxZdalOGnZFZ1BwC4H04Xeojh/zx7k+XW9UIq9f7ComKt+TVN1zasLXugrzNL00uLdjl1fwAAVAeMZHmYo5lnKvW+D1fv119nbtbgD527ZlZBUbFT9wcAQHXBSBbK5d0VeyVJu65g/lR6Tr78fb3k7+OtEf/couW7jjmrPAAASrF43jshy9Nk5OZX6n2n84uu6Ljf/XxEY2afXcX98VtaErAAAG6PkOVh3l2x74r3sSs1S60iyze369Mfk1RUbOiFBYmOba8s3n3FNQAAUN0RslBhyxKPKaZ2kHLyClU3JKDEa0cycvXJ2iTd16WRktJy9Px/dlpUJQAA1iJkoVKumbxU+UXF2vhkD0WEBOhkTr5qB/lq+GdbtDMlS/9Ym2R1iQAAWMqtri6cNGmSbDZbiUdkZKTjdcMwNGnSJEVFRSkwMFA33nijduzYUWIfeXl5euSRRxQWFqbg4GANGjRIhw8fLtEmPT1dQ4cOld1ul91u19ChQ5WRkVEVXaw28v93VeBPB9PV4/WVuvb/lur//puonSlZFlcGAED14FYhS5KuuuoqpaSkOB7btm1zvPbKK69o2rRpeuedd7R582ZFRkaqV69eys7+/Yq5sWPHav78+ZozZ47Wrl2rU6dOacCAASoq+n3i95AhQ5SQkKDFixdr8eLFSkhI0NChQ6u0n1Y6/zYFhcWG9h3PkSR98iOjVwAAnON2pwt9fHxKjF6dYxiG3nzzTT311FO67bbbJEmfffaZIiIi9OWXX2rkyJHKzMzUjBkz9Pnnn6tnz56SpC+++EIxMTH64Ycf1KdPHyUmJmrx4sXasGGDOnbsKEn6+OOP1blzZ+3evVstW7asus5aJOP07zeOrn7rxwMAUD243UjWr7/+qqioKDVu3Fh333239u/fL0lKSkpSamqqevfu7Wjr7++v7t27a926dZKkrVu3qqCgoESbqKgotWnTxtFm/fr1stvtjoAlSZ06dZLdbne0KUteXp6ysrJKPFzVR6v3O/698JcUCysBAKD6cquQ1bFjR/3zn//U999/r48//lipqanq0qWLTpw4odTUVElSREREifdEREQ4XktNTZWfn59q1659yTZ169Ytdey6des62pRl6tSpjjlcdrtdMTExV9TX6mLxjov3GQAAT+ZWIatv3766/fbb1bZtW/Xs2VMLFiyQdPa04Dk2W8n1Xw3DKLXtQhe2Kav95fYzceJEZWZmOh6HDh0qV58AAIBrcquQdaHg4GC1bdtWv/76q2Oe1oWjTceOHXOMbkVGRio/P1/p6emXbHP06NFSxzp+/HipUbLz+fv7KyQkpMQDAAC4L7cOWXl5eUpMTFS9evXUuHFjRUZGaunSpY7X8/PztWrVKnXp0kWS1KFDB/n6+pZok5KSou3btzvadO7cWZmZmdq0aZOjzcaNG5WZmeloAwAArHeZE1Wmc6urC8ePH6+BAweqQYMGOnbsmF544QVlZWXpvvvuk81m09ixYzVlyhQ1b95czZs315QpUxQUFKQhQ4ZIkux2ux544AE99thjCg0NVZ06dTR+/HjH6UdJat26tW655RaNGDFCH374oSTpwQcf1IABAzziykIAAFA+bhWyDh8+rHvuuUdpaWkKDw9Xp06dtGHDBjVs2FCS9Pjjjys3N1ejR49Wenq6OnbsqCVLlqhmzZqOfbzxxhvy8fHRXXfdpdzcXPXo0UMzZ86Ut7e3o82sWbM0ZswYx1WIgwYN0jvvvFO1nQUAANWazTAMljqyQFZWlux2uzIzM6tkflajCQtMPwYAANXJre2j9Obd1zh1nxX5/nbrOVkAAMBzfZtwxNLjE7IAAABMQMgCAAAwASELAADABIQsAAAAExCyAAAATEDIAgAAMAEhCwAAwASELAAAABMQsgAAAExAyAIAADABIQsAAMAEhCwPkJlbYHUJAAB4HEKWB5j8n51WlwAAgMchZHmAnw9nWF0CAAAeh5AFAABgAkIWAACACQhZAAAAJiBkeQDDMKwuAQAAj0PIAgAAMAEhCwAAwASELA/AyUIAAKoeIcsTkLIAAKhyhCwAAAATELIAAABMQMjyAJwtBACg6hGyAAAATEDIAgAAMAEhCwAAwASELAAAABMQsjwA9y4EAKDqEbIAAABMQMjyAEez8qwuAQAAj0PIcnOGYSi3oMjqMgAA8DiELDfHdCwAAKxByHJzZCwAAKxByHJzxQxlAQBgCUKWmyNjAQBgDUKWmzM4YQgAgCUIWW6OkSwAAKxByHJzhCwAAKxByHJzTHwHAMAahCw3t2h7qtUlAADgkQhZbm78Vz9bXQIAAB6JkAUAAGACQhYAAIAJCFkAAAAmIGS5sUnf7bC6BAAAPBYhy43NXHfA6hIAAPBYhCwAAAATELIAAABMQMgCAAAwASHLTc3aeNDqEgAA8GiELDf1xtI9VpcAAIBHI2S5qbRT+VaXAACAR/Op6BsMw9CqVau0Zs0aHThwQKdPn1Z4eLiuueYa9ezZUzExMWbUWW299957evXVV5WSkqKrrrpKb775prp162Z1WQAAwGLlHsnKzc3VlClTFBMTo759+2rBggXKyMiQt7e39u7dq+eee06NGzdWv379tGHDBjNrrjbmzp2rsWPH6qmnnlJ8fLy6deumvn37Kjk52erSAACAxcodslq0aKGffvpJH3zwgbKysrRhwwbNmzdPX3zxhRYuXKjk5GTt27dP3bp10+DBg/Xxxx+bWXe1MG3aND3wwAMaPny4WrdurTfffFMxMTF6//33rS4NAABYrNynCxctWqQ2bdpcsk3Dhg01ceJEPfbYYzp40L2vbsvPz9fWrVs1YcKEEtt79+6tdevWlWqfl5envLw8x/OsrCxT6tp84KTu/GC9KfsGAADlV+6RrPMDVnJysgzDKNXGMAwlJyfLz89PzZs3d06F1VRaWpqKiooUERFRYntERIRSU1NLtZ86darsdrvjYdbcNV9vrmUAAKA6qNQ3cuPGjXX8+PFS20+ePKnGjRtfcVGuxGazlXhuGEapbZI0ceJEZWZmOh6HDh0ypZ72MbX0yh1Xm7JvAABQfpUKWRcLEqdOnVJAQMAVF+UKwsLC5O3tXWrU6tixY6VGtyTJ399fISEhJR5muSsuRg3qBJm2fwAAcHkVWsJh3Lhxks6O3jzzzDMKCvr9i7yoqEgbN25U+/btnVpgdeXn56cOHTpo6dKl+tOf/uTYvnTpUv3xj3+0sDIAAFAdVChkxcfHSzo7krVt2zb5+fk5XvPz81O7du00fvx451ZYjY0bN05Dhw5VXFycOnfurI8++kjJyckaNWqU1aXJUOk5cwAAoOpUKGStWLFCkvTXv/5Vb731lqmnvFzB4MGDdeLECU2ePFkpKSlq06aNFi5cqIYNG1pdmoqLra4AAADPZjPKukwQpsvKypLdbldmZqYpYbXL1GU6knnG6fsFAMCVHHipv1P3V5Hv73JPfB81alS5r4ibO3euZs2aVd5dAwAAuJ1yny4MDw9XmzZt1KVLFw0aNEhxcXGKiopSQECA0tPTtXPnTq1du1azZ89WdHS0PvroIzPrxmW8fMfVGjpjk9VlAADgsSp0uvDYsWOaMWOG5syZo+3bt5d4rWbNmurZs6cefPBB9e7d2+mFuhuzTxdK0j/XH9Cz/95hyr4BAHAFVp4urNDE97p162rixImaOHGiMjIydPDgQeXm5iosLExNmzaVzWZTQkLCldQOJ2oRUdPqEgAA8FgVClnnq1WrlmrVqiVJyszM1Pvvv68ZM2YoISFBRUVFzqoPAADAJV3Rje6WL1+uv/zlL6pXr56mT5+uvn37asuWLc6qDVeodaRnL7EBAICVKjySdfjwYc2cOVOffPKJcnJydNddd6mgoEDz5s1TbGysGTWikuxBvlaXAACAx6rQSFa/fv0UGxurnTt3avr06Tpy5IimT59uVm1wgibhwVaXAACAR6pQyFqyZImGDx+u559/Xv3795e3t7dZdcFJPh32B6tLAADAI1UoZK1Zs0bZ2dmKi4tTx44d9c477+j48eNm1QYnaBjKSBYAAFaoUMjq3LmzPv74Y6WkpGjkyJGaM2eO6tevr+LiYi1dulTZ2dlm1QkAAOBSKnV1YVBQkO6//36tXbtW27Zt02OPPaaXXnpJdevW1aBBg5xdIwAAgMu5oiUcJKlly5Z65ZVXdPjwYc2ePdsZNQEAALi8Kw5Z53h7e+vWW2/Vd99956xdAgAAuCynhSwAAAD8jpAFAABgAkIWAACACQhZAAAAJiBkAQAAmICQBQAAYAJCFgAAgAkIWQAAACYgZHmAPldFWF0CAAAeh5DlAYL9fKwuAQAAj0PI8gCG1QUAAOCBCFkAAAAmIGQBAAC31KZ+iKXHJ2QBAACYgJAFAABgAkIWAACACQhZHsAwuL4QAICqRsgCAAAwASHLA9hsNqtLAACgytlk7fcfIcsDcLoQAICqR8gCAAAwASELAADABIQsAAAAExCyAAAATEDI8gBMewcAoOoRsgAAgFsyLB5mIGQBAACYgJAFAABgAkIWAABwS6z4DgAA4IYIWR6ghr+P1SUAAOBxCFkeYFyvFlaXAACAxyFkeYDQGv5WlwAAgMchZAEAAJiAkAUAAGACQhYAAIAJCFkAAAAmIGQBAAC3ZLN2LVJCFgAAgBkIWQAAACYgZAEAAJjArUJWo0aNZLPZSjwmTJhQok1ycrIGDhyo4OBghYWFacyYMcrPzy/RZtu2berevbsCAwNVv359TZ48WYZhlGizatUqdejQQQEBAWrSpIk++OAD0/sHAABch9vd1G7y5MkaMWKE43mNGjUc/y4qKlL//v0VHh6utWvX6sSJE7rvvvtkGIamT58uScrKylKvXr100003afPmzdqzZ4+GDRum4OBgPfbYY5KkpKQk9evXTyNGjNAXX3yhH3/8UaNHj1Z4eLhuv/32qu0wAAAo0wXjI1XO7UJWzZo1FRkZWeZrS5Ys0c6dO3Xo0CFFRUVJkl5//XUNGzZML774okJCQjRr1iydOXNGM2fOlL+/v9q0aaM9e/Zo2rRpGjdunGw2mz744AM1aNBAb775piSpdevW2rJli1577TVCFgAAkORmpwsl6eWXX1ZoaKjat2+vF198scSpwPXr16tNmzaOgCVJffr0UV5enrZu3epo0717d/n7+5doc+TIER04cMDRpnfv3iWO26dPH23ZskUFBQVl1pWXl6esrKwSDwAA4L7cKmT97W9/05w5c7RixQo9/PDDevPNNzV69GjH66mpqYqIiCjxntq1a8vPz0+pqakXbXPu+eXaFBYWKi0trczapk6dKrvd7njExMRcWWcBAEC1Vu1D1qRJk0pNZr/wsWXLFknSo48+qu7du+vqq6/W8OHD9cEHH2jGjBk6ceKEY3+2MlYmMwyjxPYL25yb9F7RNuebOHGiMjMzHY9Dhw5V5McAAABcTLWfk/Xwww/r7rvvvmSbRo0albm9U6dOkqS9e/cqNDRUkZGR2rhxY4k26enpKigocIxMRUZGOkaszjl27JgkXbaNj4+PQkNDy6zF39+/xClIAABgLqtXfK/2ISssLExhYWGVem98fLwkqV69epKkzp0768UXX1RKSopj25IlS+Tv768OHTo42jz55JPKz8+Xn5+fo01UVJQjzHXu3Fn/+c9/ShxryZIliouLk6+vb6VqBQAA7qXany4sr/Xr1+uNN95QQkKCkpKS9K9//UsjR47UoEGD1KBBA0lS7969FRsbq6FDhyo+Pl7Lli3T+PHjNWLECIWEhEiShgwZIn9/fw0bNkzbt2/X/PnzNWXKFMeVhZI0atQoHTx4UOPGjVNiYqI++eQTzZgxQ+PHj7es/wAAoHqp9iNZ5eXv76+5c+fq+eefV15enho2bKgRI0bo8ccfd7Tx9vbWggULNHr0aHXt2lWBgYEaMmSIXnvtNUcbu92upUuX6qGHHlJcXJxq166tcePGady4cY42jRs31sKFC/Xoo4/q3XffVVRUlN5++22WbwAAAA4248KlzFElsrKyZLfblZmZ6RhFM1OjCQtMPwYAANXJ1dF2fffw9U7dZ0W+v93mdCEAAEB1QsgCAAAwASELAADABIQsAAAAExCyAAAATEDIAgAAbsniBd8JWQAAAGYgZHmYpuHBVpcAAECVsHohUEKWh2lb3251CQAAeARCFgAAgAkIWQAAACYgZHkYm83qay0AAPAMhCwAAAATELIAAABMQMgCAAAwASELAAC4JatnIROyPMTDNzVTTX8fje3Z3OpSAADwCD5WF4CqMb5PS43r1UJeXlbnegAAPAMjWR6EgAUAQNUhZAEAAJiAkAUAAGACQhYqrFVkTatLAACg2iNkocKahAfrnusaSJLax9RSkJ+3xRUBAFD9ELJQLo1Cg0o8n3pbW+2c3EfzR3dRr9gIi6oCAKD6YgkHlIufT+k8HuTHfz4AAFwMI1koF5tsGhwXI0kafWMzi6sBAKD6YygC5fbS7W313KBYRrAAACgHRrI8UHAlJ6rbbLYyA9afrql/pSUBAOB2CFke6KGbnXu678aWdfX92Bu0/LHuiq0X4tR9AwDgqjjv44EMw/n7bMnaWQAAlMBIFsqlTrCf1SUAAOBSCFkol1fvvLpc7Qb/IcbkSgAAcA2ELFxWt+Zhiq4ddPmGkoZ2amhyNQAAuAbmZHkgm6187fy8vRT/bK8K3TbHy6ucOwcAwM0xkoVLCvb3ka28qewC93VmVAsA4LkIWbioQe2jruj9IYG+TqoEAIBKqOQggbMQsjxQeZdwmPzHqyq1/x6t6kqS7opjEjwAwHMxJwsXVdnb5/zjvjjlFhRx+x0AgEdjJAtOd7Hb7wAA4EkIWQAAACYgZHm4mDqBJZ7f37WxU/ff56oIp+4PAABXQcjycN4XXHnRPKKGU/f/xuD2Gtqpob4c0dGp+wUA4LLMuFlvBTBxxgPVDqq6+xAG+fno/25tU2XHAwCgumAkywPd0SHa8e9rG9Qu8VqryJqmHbdJeLBp+wYAoLphJMsD+fl4aflj3fXdz0f0166N9U38b47XrmlQW/+4N04NQst3r8KK4IY7AIAqxWKksEKT8Boa27OF7GWsyt4zNkItIpw/ovVU/9ZO3ycAANUVIQtV5uZWEfplUm8deKm/1aUAAGA6QhaqVEjA2ZGzrs1CLa4EAABzEbJgien3XGt1CQAAmIqQBUvUCa66ZSQAALACIQuWeevu9urchNOGAAD3RMiCZf7Yvr5mP9jJ6jIAADAFIQsa0e3s/QobmbA2FgAAnorFSKGn+sdqfJ+W8vfxtuT4Xjap2NrbSwEA4HSMZEGSLAtYkvTvh6637NgAAPdl9Z1GCFmwXMMwTlMCANyPy4SsF198UV26dFFQUJBq1apVZpvk5GQNHDhQwcHBCgsL05gxY5Sfn1+izbZt29S9e3cFBgaqfv36mjx5sgyj5LmqVatWqUOHDgoICFCTJk30wQcflDrWvHnzFBsbK39/f8XGxmr+/PlO66unCfbjrDUAwP24TMjKz8/XnXfeqf/3//5fma8XFRWpf//+ysnJ0dq1azVnzhzNmzdPjz32mKNNVlaWevXqpaioKG3evFnTp0/Xa6+9pmnTpjnaJCUlqV+/furWrZvi4+P15JNPasyYMZo3b56jzfr16zV48GANHTpUP//8s4YOHaq77rpLGzduNO8H4Ma8vWza8XwfXd8szOpSAABwGptx4TBONTdz5kyNHTtWGRkZJbYvWrRIAwYM0KFDhxQVFSVJmjNnjoYNG6Zjx44pJCRE77//viZOnKijR4/K399fkvTSSy9p+vTpOnz4sGw2m5544gl99913SkxMdOx71KhR+vnnn7V+/XpJ0uDBg5WVlaVFixY52txyyy2qXbu2Zs+eXWbdeXl5ysvLczzPyspSTEyMMjMzFRIS4pSfjatLTMlS37fWWF0GAMBNtIuppX8/1NWp+8zKypLdbi/X97fLjGRdzvr169WmTRtHwJKkPn36KC8vT1u3bnW06d69uyNgnWtz5MgRHThwwNGmd+/eJfbdp08fbdmyRQUFBZdss27duovWN3XqVNntdscjJibmivrrjlrXC1HjsGCrywAAwCncJmSlpqYqIiKixLbatWvLz89PqampF21z7vnl2hQWFiotLe2Sbc7toywTJ05UZmam43Ho0KFK9NL9TflTW6tLAADAKSwNWZMmTZLNZrvkY8uWLeXen81W+mJNwzBKbL+wzbmzpc5oU9bxz/H391dISEiJB0qLa1Tb6hIAAHAKSy/revjhh3X33Xdfsk2jRo3Kta/IyMhSE8/T09NVUFDgGHWKjIwsNdp07NgxSbpsGx8fH4WGhl6yzYWjW6g4X28vrXn8JnV7ZYXVpQAAcEUsHckKCwtTq1atLvkICAgo1746d+6s7du3KyUlxbFtyZIl8vf3V4cOHRxtVq9eXWJZhyVLligqKsoR5jp37qylS5eW2PeSJUsUFxcnX1/fS7bp0qVLhX8GKC2mTpAOvNTf6jIAALgiLjMnKzk5WQkJCUpOTlZRUZESEhKUkJCgU6dOSZJ69+6t2NhYDR06VPHx8Vq2bJnGjx+vESNGOE7NDRkyRP7+/ho2bJi2b9+u+fPna8qUKRo3bpzjVN+oUaN08OBBjRs3TomJifrkk080Y8YMjR8/3lHL3/72Ny1ZskQvv/yydu3apZdfflk//PCDxo4dW+U/F3fWLtpudQkAABdm9YrvLrOEw7Bhw/TZZ5+V2r5ixQrdeOONks4GsdGjR2v58uUKDAzUkCFD9Nprr5W4mnDbtm166KGHtGnTJtWuXVujRo3Ss88+W2I+1apVq/Too49qx44dioqK0hNPPKFRo0aVOO7XX3+tp59+Wvv371fTpk314osv6rbbbit3fypyCain+jb+N42dm2B1GQAAF9U+ppa+tXAJB5cJWe6GkHV5RcWG7vtkk9buTbO6FACAC7I6ZLnM6UJ4Hm8vm74Y3lELxnADaQCA6yFkodq7KsquNwe3t7oMAAAqhJAFl3DrNfWtLgEAgAohZAEAAJiAkAWX8XT/1laXAABAuVm64jtQEcO7NVGXpmGyB/nquX9v1w+Jx6wuCQCAi2IkCy4lNipE9WsF6rrGdawuBQCASyJkwSX9uWNDtYu266qoEP3j3jirywEAVEM2i5d853QhXFKwv4/+/fDv62fNebCT3lu5TxE1/dUkvIZeXrzLwuoAANWB1cutE7LgFjo1CVWnJqGO55m5Bfpg1T4LKwIAeDpOF8ItTejbSomTb9GBl/rrppbhVpcDAPBAhCy4rUA/b0nSjPv+oNV/v8niagAAnoaQBbfn5WVTg9AgbXyyh267pr7m/b8uahdtV6/YCKtLAwC4MeZkwWNEhARo2v/ugfjtQ11ls9lkGIZeX7JHhcUGc7gAAE5FyIJHsv3vul6bzabxfVpKkm6/tr76vLlaxRZfjQIAcA+cLgT+p3lETW18sqfVZQAA3AQhCzhPeE1/bZjYQ9sm9bZ8ETsAgGsjZAEXiLQHqGaAr34Y192xrWFokIUVAQAqw+o/lpmTBVxE0/Aa2vRUD9X095Wfj5c+XrNfLy1iJXkAQPkwkgVcQt2aAQr085a3l02jujfVugk364YWLG4KALg8RrKACoiqFah/3n+dvt56WCt3H9P/u7GpouyBmvzfnZof/5vV5QEAqhFGsoBKuKNDtN4Zcq2uirKrdrCfnhsYK5tNuqZBLe14vo/V5QEAqgFGsgAnqBXkp8TJt8jP20teXiVnWj5wfWPNWJtkUWUAAKswkgU4SYCvtyNg/b1PS/l62/Sfh6/XMwNitfkp1t8CAE/DSBZggoduaqaRNzSRj/fZv2PCavhZXBEAVF91a/rryxEdFRrsr58PZ2jYp5utLskpCFmASc4FLOns7Xv2T+mnJk8utLAiALBe/7b1dOs19dW8bg29texX7U/L0azhHVXD/2wkubFlXa2bcLPmbErW3dc10NGsMxo7N0E1A3w0+Y9tdG2D2vo2/jet2nO82l9wZDMMgzu1WSArK0t2u12ZmZkKCQmxuhxUkbRTeYp74Qery0AVefWOq/X3r3+RJCVOvkWtn11scUVwNSEBPgqt4a+ktByn7K97i3Ct2nNcvWIj9Nod7ZRwOEPr9qUp6XiOluw86pRjnM/fx0t/69lc3yUc0ecPdFStIF/5ejtvplL2mQKt2nNc3VuE6+6PNmjHkSxJkreXTcWGoW9Hd1W7mFpOO55Use9vQpZFCFmea+eRLPV7e43VZaAKHHipvyTJMAzZbDa9vexX/efnI+raLEydmoRq9qZkrdpzXJL0wV+u1agvfrKy3BK6NQ/Tml/TSmwb2b2JsnILNXtTsmNbeE1/Hc/Oq+ryqpUBV9fTf39JkSRN6NtKDeoE6cUFifotI1eStPaJm3T9yyskSSvH36g1e9P0zLfbL7q/PldF6N7OjdQuppZq+PvoVF6hXlyQqNmbkjWwXZRGdW+ir7Yc1qo9x/Xnjg30woJEvXRbW7VvUEuFRYbeWLpHA9rV05cbk7X5QLoahwWrX9tIPdqzRYkR9gttSjqpQydPq/dVEeo0ZZly8otKtbm+WZjW7k0r491S/VqB+i0jV2/d3V5/m5MgSbqpZbg+/et15fo5XqmsMwVatzdNXZuFqWaArwqKip0a6BzHIWRVf4Qsz9ZowgKrS4CkFhE1tOfoqQq9p3W9EDWoE6i/92mlZnVrKON0vp759w7VDvJVTO0gdW8Zrodm/aQHb2iiO+NiLrmvnLxCvbAgUf3b1tP1zcO0eHuq1u9L0186NVSvN1ZLkp4dEKvjp/I0rEsjTfxmm5bvOibp7Jf5S4t2yd/HSz+M6y57kK92p2arXXQt5eYXKSe/UF1eWl7mcdc+cZPq1wpU44m/n75+8IYm+mj1fknSH9tH6a27r3GEwwsZhqGfktO19WC6hl/fRF5eNkfbw+mnNW3JHm1MOukIGX9oVFubD6RX6OdcGed+JlVhVPemeuKWljqRk6+wGv4yDEOn84sU/L9TXkXFhkb8c4ti64VofJ+WKi42Slx5PG/rYdWrFaAODWvL38dbszcl6+dDGYqNCtG9nRuVeczM0wUKCfRx/E7O/cxz84sU6Oddqr1hGDqcnqvo2oFl/h4vJTO3QDPWJqlJWLASDmXoL50ayssmNQ4L1ic/HlCUPUBeXjYt+CVFi3ekqluzMH18b5wycgtUJ9hPM9Ym6aPV+zTnwc5qHBZcoWNXd4QsF0DI8mzHs/P0bfxvur1DtK79v6WO7T1b19UPiWe/RNvWt+umVnXl7+OlV7/fbVWplnqsVwv1bRupntNWX9F+2sXUUrCft9btOyFfb5tm3PcHXd8sTF5eNmWcztf237IUEeKv3zJyVVhkaPg/tzjeu2L8jVqWeFS3XxstH2+bagb4Xmm3ysUwDBmGSnwxG4ah7LxChZSzhpTMXL2zfK8Cfb01pGMDFRQZKigqVpv6dsf+ss4U6sSpPDUJr6EVu45p22+ZeuTmZhX+Ur5Qbn6RWj+7WGE1/LTl6V5av++EDp08rWLD0G8Zufp8w0FlnC647H7u7BCtr7Ye1lt3t9eNLeuq05RlCvb3Ue+rIvTlxrMjaiNvaKKHbm6mkABfFRYV66fkDEWGBGhr8kk9OvfnK+pHWT6+N07dW4TLz4cL9C/lYiHd1RGyXAAhC+cs2pait5b9qneGXKNAPx91/d/oQ9LUfo4PqHV70zTuXz8rNeuMpLNhbNrg9pqyIFFzNh+yrPZzomsHqmvTMG05eFL7jp+dO/Lin9ooMSVLX2z4/dTSIzc30/Tle0u8t1aQrx66sZleXJgo6ezyF1G1AnRD83CF1vCXJO09dko9p6266PE7NamjDftPlvnaY71a6JEezSVJ+YXF5fpifGnRLn2wap9jRAeVczq/UD5eXhf9mV84ouvrbdO6CT0U4Ot10TCbX1gsX2+bbLazo2fnRpIu5ce9aVq7N03dW4SrYWiQzhQU68e9aXr6glN2/j5e6tk6QgmHMjSxXyv1b1tPNptN+YXFWr//hN5bsVfDujRS37b1KvBTgLshZLkAQhYuZv/xU7IH+joCxvlSM8/ou59/0+C4BrIHnf0S2nLgpD5bf1D/+fmIJCnIz1tP9mut9ftOaMG2lEvOoaiskd2b6MNVZ08tTezbSiO7N3W8tnTnUe1KydLD/xsNScnM1YG002ocFqxIe4CKiw1l5haodnDJZS0uN3/ih51HtXLPMT0zIFaJKdn65qfDsgf6ql10LfWMjXB8+X6+4aB+PXpKzw6M1e7UbMXWCym1QOzlFBUb+vlwhtpE2RmtMNHi7Sk6kZOv3rGRWrv3uPq2qacA39KnvcySdipPryzepSMZZzSyexN1a859SXF5hCwXQMiCsxmGoeOn8lS3ZkCZr50bFevzxmrtPpotby+b/v1QV8XWC9ELCxL1yY9JCvD1UmGRocLi0h8LXZuFKjElW/+4L07XNqito1lntDHppPq2iTRlcikAVEeELBdAyIJVTucXat+xHLWpH1JqvsS5ybkb9p/Q/TM3q06wn65rXEf929ZTj9YRFlUMANUHIcsFELIAAHA9Ffn+ZowfAADABIQsAAAAExCyAAAATEDIAgAAMAEhCwAAwASELAAAABMQsgAAAExAyAIAADABIQsAAMAEhCwAAAATELIAAABMQMgCAAAwASELAADABIQsAAAAE/hYXYCnMgxDkpSVlWVxJQAAoLzOfW+f+x6/FEKWRbKzsyVJMTExFlcCAAAqKjs7W3a7/ZJtbEZ5ohicrri4WEeOHFHNmjVls9mcuu+srCzFxMTo0KFDCgkJceq+qytP67On9Veiz57QZ0/rr0SfXbHPhmEoOztbUVFR8vK69KwrRrIs4uXlpejoaFOPERIS4pL/AV8JT+uzp/VXos+ewNP6K9FnV3O5EaxzmPgOAABgAkIWAACACQhZbsjf31/PPfec/P39rS6lynhanz2tvxJ99gSe1l+JPrs7Jr4DAACYgJEsAAAAExCyAAAATEDIAgAAMAEhCwAAwASELBf13nvvqXHjxgoICFCHDh20Zs2aS7ZftWqVOnTooICAADVp0kQffPBBFVXqHBXp7zfffKNevXopPDxcISEh6ty5s77//vsqrNY5Kvo7PufHH3+Uj4+P2rdvb26BJqhon/Py8vTUU0+pYcOG8vf3V9OmTfXJJ59UUbVXrqL9nTVrltq1a6egoCDVq1dPf/3rX3XixIkqqvbKrV69WgMHDlRUVJRsNpu+/fbby77HlT+7Ktpfd/jsqszv+BxX/uy6GEKWC5o7d67Gjh2rp556SvHx8erWrZv69u2r5OTkMtsnJSWpX79+6tatm+Lj4/Xkk09qzJgxmjdvXhVXXjkV7e/q1avVq1cvLVy4UFu3btVNN92kgQMHKj4+voorr7yK9vmczMxM3XvvverRo0cVVeo8lenzXXfdpWXLlmnGjBnavXu3Zs+erVatWlVh1ZVX0f6uXbtW9957rx544AHt2LFDX331lTZv3qzhw4dXceWVl5OTo3bt2umdd94pV3tX/+yqaH/d4bOron0+x5U/uy7JgMu57rrrjFGjRpXY1qpVK2PChAlltn/88ceNVq1aldg2cuRIo1OnTqbV6EwV7W9ZYmNjjeeff97ZpZmmsn0ePHiw8fTTTxvPPfec0a5dOxMrdL6K9nnRokWG3W43Tpw4URXlOV1F+/vqq68aTZo0KbHt7bffNqKjo02r0UySjPnz51+yjat/dp2vPP0ti6t9dp2vIn125c+uS2Eky8Xk5+dr69at6t27d4ntvXv31rp168p8z/r160u179Onj7Zs2aKCggLTanWGyvT3QsXFxcrOzladOnXMKNHpKtvnTz/9VPv27dNzzz1ndolOV5k+f/fdd4qLi9Mrr7yi+vXrq0WLFho/frxyc3OrouQrUpn+dunSRYcPH9bChQtlGIaOHj2qr7/+Wv3796+Kki3hyp9dzuBqn12V5cqfXZfDDaJdTFpamoqKihQREVFie0REhFJTU8t8T2pqapntCwsLlZaWpnr16plW75WqTH8v9PrrrysnJ0d33XWXGSU6XWX6/Ouvv2rChAlas2aNfHxc73/ryvR5//79Wrt2rQICAjR//nylpaVp9OjROnnyZLWfl1WZ/nbp0kWzZs3S4MGDdebMGRUWFmrQoEGaPn16VZRsCVf+7HIGV/vsqgxX/+y6HEayXJTNZivx3DCMUtsu176s7dVVRft7zuzZszVp0iTNnTtXdevWNas8U5S3z0VFRRoyZIief/55tWjRoqrKM0VFfs/FxcWy2WyaNWuWrrvuOvXr10/Tpk3TzJkzXWI0S6pYf3fu3KkxY8bo2Wef1datW7V48WIlJSVp1KhRVVGqZVz9s6uyXPmzq7zc6bPrYtwvNrq5sLAweXt7l/pr99ixY6X+4jsnMjKyzPY+Pj4KDQ01rVZnqEx/z5k7d64eeOABffXVV+rZs6eZZTpVRfucnZ2tLVu2KD4+Xg8//LCkswHEMAz5+PhoyZIluvnmm6uk9sqqzO+5Xr16ql+/vux2u2Nb69atZRiGDh8+rObNm5ta85WoTH+nTp2qrl276u9//7sk6eqrr1ZwcLC6deumF154wS1HdVz5s+tKuOpnV0W5w2fX5TCS5WL8/PzUoUMHLV26tMT2pUuXqkuXLmW+p3PnzqXaL1myRHFxcfL19TWtVmeoTH+ls38FDhs2TF9++aXLzVmpaJ9DQkK0bds2JSQkOB6jRo1Sy5YtlZCQoI4dO1ZV6ZVWmd9z165ddeTIEZ06dcqxbc+ePfLy8lJ0dLSp9V6pyvT39OnT8vIq+ZHt7e0t6ffRHXfjyp9dleXKn10V5Q6fXZdlzXx7XIk5c+YYvr6+xowZM4ydO3caY8eONYKDg40DBw4YhmEYEyZMMIYOHepov3//fiMoKMh49NFHjZ07dxozZswwfH19ja+//tqqLlRIRfv75ZdfGj4+Psa7775rpKSkOB4ZGRlWdaHCKtrnC7niFToV7XN2drYRHR1t3HHHHcaOHTuMVatWGc2bNzeGDx9uVRcqpKL9/fTTTw0fHx/jvffeM/bt22esXbvWiIuLM6677jqrulBh2dnZRnx8vBEfH29IMqZNm2bEx8cbBw8eNAzD/T67Ktpfd/jsqmifL+SKn12XQshyUe+++67RsGFDw8/Pz7j22muNVatWOV677777jO7du5dov3LlSuOaa64x/Pz8jEaNGhnvv/9+FVd8ZSrS3+7duxuSSj3uu+++qi/8ClT0d3w+V/2gqmifExMTjZ49exqBgYFGdHS0MW7cOOP06dNVXHXlVbS/b7/9thEbG2sEBgYa9erVM/785z8bhw8fruKqK2/FihWX/H/T3T67Ktpfd/jsqszv+Hyu+tl1MTbDcNNxZgAAAAsxJwsAAMAEhCwAAAATELIAAABMQMgCAAAwASELAADABIQsAAAAExCyAAAATEDIAgAAMAEhCwCuwMqVK2Wz2WSz2XTrrbeW6z2TJk1yvOfNN980tT4A1iFkAUAF3HjjjRo7dmyp7bt379bMmTPLtY/x48crJSWl2t/IGsCV8bG6AABwB3Xr1lWtWrXK1bZGjRqqUaOGvL29zS0KgKUYyQKAcho2bJhWrVqlt956y3G678CBA2W2/frrr9W2bVsFBgYqNDRUPXv2VE5OTtUWDMBShCwAKKe33npLnTt31ogRI5SSkqKUlBTFxMSUapeSkqJ77rlH999/vxITE7Vy5UrddtttMgzDgqoBWIXThQBQTna7XX5+fgoKClJkZKQkadeuXaXapaSkqLCwULfddpsaNmwoSWrbtm2V1grAeoxkAYCTtWvXTj169FDbtm1155136uOPP1Z6errVZQGoYoQsAHAyb29vLV26VIsWLVJsbKymT5+uli1bKikpyerSAFQhQhYAVICfn5+Kioou285ms6lr1656/vnnFR8fLz8/P82fP78KKgRQXTAnCwAqoFGjRtq4caMOHDigGjVqqLi4uFSbjRs3atmyZerdu7fq1q2rjRs36vjx42rdurUFFQOwCiNZAFAB48ePl7e3t2JjYxUeHq7k5ORSbUJCQrR69Wr169dPLVq00NNPP63XX39dffv2taBiAFZhJAsAKqBFixZav3694/nKlStLtWndurUWL15chVUBqI4YyQIAJ4iOjtY999xTrrZTpkxRjRo1yhwFA+A+bAar4wFApeXm5uq3336TdPZ2OefWz7qUkydP6uTJk5Kk8PBw2e12U2sEYA1CFgAAgAk4XQgAAGACQhYAAIAJCFkAAAAmIGQBAACYgJAFAABgAkIWAACACQhZAAAAJiBkAQAAmOD/A13vluBdYqtjAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "data = np.loadtxt(\"trumpet.txt\")\n", "\n", "t = np.linspace(0, 2**16/44.1E3, 2**16)\n", "\n", "plt.plot(t, data)\n", "plt.xlabel(\"t[s]\")\n", "plt.ylabel(\"A(t)\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "6e8832e8", "metadata": {}, "source": [ "Ici on voit plutôt l'enveloppe du signal. Pour mieux résoudre qu'il s'agit en fait d'une onde, on va magnifier une partie de l'échantillon:" ] }, { "cell_type": "code", "execution_count": 2, "id": "293fe699", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(range(20000, 21000), data[20000:21000])\n", "plt.xlabel(\"t\")\n", "plt.ylabel(\"A(t)\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "2915736e", "metadata": {}, "source": [ "Quelle note joue la trompette? Pour le savoir, il faut effectuer une transformation de Fourier discrète et identifier la fréquence dominante du signal. Vu que l'échantillon est assez grand avec 65536 points de données, il convient d'utiliser la méthode de la transformation de Fourier rapide." ] }, { "cell_type": "code", "execution_count": 3, "id": "475cd30c", "metadata": {}, "outputs": [], "source": [ "def fft(phi): # \"fast Fourier transform\" ou TFD rapide\n", " N = len(phi)\n", " if N == 1:\n", " return phi\n", " phi_p = phi[::2] # les composantes de x avec indices pairs\n", " phi_i = phi[1::2] # les composantes avec indices impairs\n", " Fphi_p = fft(phi_p) # calcul récursif de la TFD\n", " Fphi_i = fft(phi_i)\n", " racines = np.exp(-2 * np.pi * 1j * np.arange(N//2) / N)\n", " c = np.empty((N), dtype=complex)\n", " c[:N//2] = Fphi_p + racines * Fphi_i\n", " c[N//2:] = Fphi_p - racines * Fphi_i\n", " return c" ] }, { "cell_type": "markdown", "id": "d7195fd5", "metadata": {}, "source": [ "On trace le spectre de puissance $|c(f)|^2$, l'intensité en fonction de la fréquence. Regardons les premiers 5000 points." ] }, { "cell_type": "code", "execution_count": 4, "id": "bf791776", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "c = fft(data) / len(data) # normaliser par 1/N\n", "power = np.abs(c)**2\n", "\n", "plt.plot(power[:5000])\n", "plt.xlabel(\"f\")\n", "plt.ylabel(\"P\")\n", "plt.title(\"Spectre de puissance d'une onde sonore\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "5bc66541", "metadata": {}, "source": [ "On identifie des maxima régulièrement espacés dont le premier correspond à la fréquence de base et ses multiples sont ses partiels harmoniques. Magnifions la région contenant le premier maximum:" ] }, { "cell_type": "code", "execution_count": 5, "id": "4a600c86", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(range(750, 800), power[750:800])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "618de82c", "metadata": {}, "source": [ "Le maximum est à $f\\approx 776$, ce qui correspond à $776\\cdot 44100\\,{\\rm Hz}/65536$:" ] }, { "cell_type": "code", "execution_count": 6, "id": "9acb9ff3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "522.18017578125\n" ] } ], "source": [ "print(776 * 44.1E3 / 2**16)" ] }, { "cell_type": "markdown", "id": "31414d17", "metadata": {}, "source": [ "La fréquence 522 Hz correspond à la note do$^4$ (plus précisément, 523.2 Hz avec un accordage standard)." ] }, { "cell_type": "code", "execution_count": null, "id": "5fb86e01", "metadata": {}, "outputs": [], "source": [] } ], "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": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }