{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Paquet d'ondes \n",
    "\n",
    "\n",
    "L'objectif est de créer un signal correspondant à un paquet d'onde de pulsation $\\omega_o$ et de durée $\\delta t$ et de tracer son spectre.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dIxhybFgy0+soIpLg1lcXkZ4SiOuhmaQp982vnKE0L4tlZbleRxGRBDclI5X1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\nwDEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1154d23c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fo=20\n",
    "wo=2*np.pi*fo\n",
    "deltaT=1\n",
    "N=5000\n",
    "\n",
    "\n",
    "Te=deltaT/N\n",
    "\n",
    "t=np.linspace(-deltaT/2,deltaT/2,N)\n",
    "\n",
    "# Création de l'enveloppe\n",
    "enveloppe=1-(np.cos(np.pi*t-np.pi/2))**12\n",
    "\n",
    "\n",
    "plt.plot(t,enveloppe)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On crée ensuite le paquet d'ondes en multipliant l'enveloppe par un cosinus de période $T_o$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yFOflxxNSOem2ehgdYDcYKn4i/p1fWTSFt3v8h16FPXPWrYahHDMGZckpb91F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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1155a9f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s=np.zeros(N)\n",
    "for i in range (N):\n",
    "    s[i]=np.cos(wo*t[i])*enveloppe[i]\n",
    "    \n",
    "plt.plot(t,s)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On calcule ensuite la transformée de Fourier du signal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1154d7198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fourier = np.fft.rfft(s)\n",
    "\n",
    "freq = np.fft.rfftfreq(N, d=Te)\n",
    "\n",
    "plt.plot(freq,np.abs(fourier[0:len(freq)])*2/N,'-o')\n",
    "plt.axis([0,50,0,1])\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Raw Cell Format",
  "colab": {
   "name": "python4tp.ipynb",
   "provenance": [],
   "toc_visible": true
  },
  "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": "3.6.1"
  },
  "toc": {
   "base_numbering": "0",
   "nav_menu": {
    "height": "369px",
    "width": "618.333px"
   },
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table des Matières",
   "title_sidebar": "Sommaire",
   "toc_cell": true,
   "toc_position": {
    "height": "calc(100% - 180px)",
    "left": "10px",
    "top": "150px",
    "width": "165px"
   },
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
