{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "RLC" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Import\n", "Python itself does not provide usefool ttools for numerical computations. So we have to import them. Ther is several ways to import modules:\n", "* You can import all the methods and functions with \n", "```python\n", "from module import *\n", "```\n", "* You can import selected functions `f1` and `f2` from a given `module` with\n", "```python\n", "from module import f1, f2\n", "```\n", "* You can import the module with a specified label with\n", "```python\n", "import module as label\n", "```" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "# Load Plot module\n", "import matplotlib.pyplot as plt\n", "# This line configures matplotlib to show figures embedded in the notebook, \n", "# instead of poping up a new window.\n", "%pylab inline\n", "# Load numerical module\n", "import numpy as np\n", "eps = np.spacing(1) # numerical precision\n", "\n", "import seaborn\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Array definition\n", "On souhaite afficher la courbe $A\\sin(2\\pi f_0t)$ pour $t\\in [0,1]$. Tout d'abord on définit un signal $s(f_0)=A\\sin(2\\pi f_0t)$, puis on l'utilise récursivement." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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50I4flVqUBXmn6wjTHgf35e8PmzGwgWZP9k7itXEc7znBhCP697Ws4JeBOJOZ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\nRDcrtUB1RfE706qBlalk2xXZ68Xe04UxJwdd3OoyuqIo8NjBfDxembc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AcgpZY30s2Fyc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Time Vector\n", "t = np.linspace(0,1,300)\n", "# Signal function\n", "A = 10 # Amplitude (V)\n", "s = lambda f0: A*np.sin(2*np.pi*f0*t)\n", "\n", "# Plot for a list of f0\n", "for f0 in np.linspace(1,2,3):\n", " label = '$f_0=$'+str(f0)\n", " plt.plot(t, s(f0), label=label)\n", "\n", "# Plot axis\n", "plt.xlabel('Temps (s)')\n", "plt.ylabel('Amplitude (V)')\n", "\n", "# Plot label and legend\n", "plt.title('$\\sin(2\\pi f_0 t)$')\n", "plt.legend(loc=0) # option loc=0 set location with minimal overlap\n", "\n", "# Show the plot\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Somme\n", "Ici on somme les trois signaux pour visualiser une forme d'onde complexe *i.e.* nonpure." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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6vjxQwJYjxbTrDNjbqZk+wZ9JY30YH+pxyR4oo9FESVUzaWdqOJxZwcm8ak7m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\nQv8HPHOSd5xha/4AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(t, [np.sum(e) for e in zip(*[s(f0) for f0 in [1,2,3]])], label='$\\sum_{i=1}^3 S_i(t)$')\n", "\n", "# Plot axis\n", "plt.xlabel('Temps (s)')\n", "plt.ylabel('Amplitude (V)')\n", "\n", "# Plot label and legend\n", "plt.title('$\\sin(2\\pi f_0 t)$')\n", "plt.legend(loc=1) # option loc=0 set location with minimal overlap\n", "\n", "# Show the plot\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }