Plotting a square wave in Python

plotSquareWave.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from IPython.html.widgets import interact, fixed\n",
    "import IPython.html.widgets as widgets\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "figsize = lambda w, h: plt.figure(figsize = (w, h))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose you have samples from a square wave. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "np.random.seed(1002342)\n",
    "nSamples = 10\n",
    "sampleTimes = np.linspace(0,1,nSamples)\n",
    "sampleValues = np.random.random(nSamples) > 0.3 # boolean values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdae67c3750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sampleTimes, sampleValues, '-ro')\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Sample Value\")\n",
    "plt.ylim(-0.1, 1.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This doesn't look like a square wave. Here's a way to fix this. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def interpolateSquare(x,y,xInterp):\n",
    "    def getValue(x,y,xi):\n",
    "        try: \n",
    "            return y[x < xi][-1]\n",
    "        except: \n",
    "            return 0 \n",
    "    return [getValue(x,y,xi) for xi in xInterp]    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nInterpolatedSamples = 1000\n",
    "newSampleTimes = np.linspace(0,1, nInterpolatedSamples)\n",
    "newSampleValues = interpolateSquare(sampleTimes, sampleValues, newSampleTimes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZmY2e1lUQwI+Kn08XVz3vB16eLiSz9FxBWNVybE9ljkHcJunFwJ8Cd9E7g+lDSaMyMxtB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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdae6a26a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sampleTimes, sampleValues, 'ro')\n",
    "plt.plot(newSampleTimes, newSampleValues, '-k')\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Sample Value\")\n",
    "plt.ylim(-0.1, 1.1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}