{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Pas de fréquentiel ici ! mais fft...\n",
    "\n",
    "Le signal \"paparite.ogg\" semble être un mélange de messages.\n",
    "Si seulement on pouvait séparer deux signaux paparfréquence non (donc pas de filtrage hein !), mais peut-être paparité ?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "[Y,Fs]=audioread(\"paparite.ogg\");\n",
    "t=((1:length(Y))-1)/Fs;\n",
    "plot(t,Y);\n",
    "title(\"Signal quelconque !\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ce signal semble pair ! Comment le vérifier ?\n",
    "Peut être en calculant la fft, mais quel lien ?\n",
    "\n",
    "Avec nos séries de Fourier ou au moins a(n) de cos c'était pour le pair et b(n) l'impair...\n",
    "D'ailleur qu'obtient-on quand on recompose que des a(n) d'un signal quelconque ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ypere=Y; #à vous de jouer et de séparer\n",
    "Yfille=Y;\n",
    "\n",
    "% help fft et ifft. mais ça fait TFD et ITFD en  gros...\n",
    "\n",
    "#une fois fin, sauvez dans un fichier audio et écoutez\n",
    "audiowrite(\"pere.ogg\",Ypere,Fs);\n",
    "audiowrite(\"fille.ogg\",Yfille,Fs);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Bravo ! Comment faire en temporel maintenant ?\n",
    "On entend un petit mélange du au bruit numérique des fft et ifft. \n",
    "\n",
    "Peut-on séparer ces deux parties mais cette fois-ci en temporel  ? Il y aurait moins de bruit...\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%Faites mieux en temporel\n",
    "Ypapa=Y;\n",
    "Ylili=Y;\n",
    "\n",
    "% vous trouvez pas ? Cherchez comment en radio on arrive à avoir un son mono sur un canal\n",
    "% et un signal sur l'autre qui permet d'avoir gauche et droite de stéréo\n",
    "\n",
    "% toujours pas ? vous retournez pas la tête... Si on vous la fait à l'envers \n",
    "% pourquoi ne pas le faire au signal...\n",
    "\n",
    "audiowrite(\"papa.ogg\",Ypapa,Fs);\n",
    "audiowrite(\"lili.ogg\",Ylili,Fs);\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "language": "octave",
   "name": "octave"
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   "help_links": [
    {
     "text": "GNU Octave",
     "url": "https://www.gnu.org/software/octave/support.html"
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    {
     "text": "Octave Kernel",
     "url": "https://github.com/Calysto/octave_kernel"
    },
    {
     "text": "MetaKernel Magics",
     "url": "https://metakernel.readthedocs.io/en/latest/source/README.html"
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   ],
   "mimetype": "text/x-octave",
   "name": "octave",
   "version": "4.2.2"
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