libiir/python/filter_analysis.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Filter analysis laboratory"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First configure the filter as desired. The filter is independent of sample rate, but is specified as a ratio to it. We use a specific value here simply to aid comprehension and label all the graph axes as desired. Setting it to 1 would be the same as specifying everything as a ratio."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import iir\n",
      "\n",
      "# change this to alter the sample rate we are displaying at\n",
      "sample_rate = 100 # Hz\n",
      "nyquist_freq = sample_rate / 2\n",
      "\n",
      "# build the filter object, fi, here\n",
      "corner_freq = 10 # Hz\n",
      "order = 4\n",
      "gain = 1.0\n",
      "filter_desc = \"butterworth_lowpass(%d, %f, %f)\" % (order, gain, corner_freq / nyquist_freq)\n",
      "print(filter_desc)\n",
      "fi = iir.Filter(filter_desc)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "butterworth_lowpass(4, 1.000000, 0.200000)\n"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we set up the plotting library and helper functions."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "import pylab\n",
      "\n",
      "# number of points to plot on graphs (arbitrary)\n",
      "num_points = 1000\n",
      "\n",
      "# helper function: calls the Filter.response() method on each member of the array\n",
      "respfunc = pylab.vectorize(lambda f: fi.response(f/sample_rate))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 66
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Filter characteristics"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "-3dB points"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "halfgain = np.array(fi.responseMinus3dB(gain)) * sample_rate\n",
      "print(halfgain)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 9.99999995]\n"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Impulse response"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# start at t=0, impulse at t=tau, end at t=10\u00d7tau\n",
      "tau = sample_rate * (1 / corner_freq) # number of samples\n",
      "\n",
      "x = pylab.hstack([pylab.zeros(tau), pylab.ones(9*tau)])\n",
      "t = pylab.linspace(0, tau / 10, x.size)\n",
      "fi2 = iir.Filter(fi)\n",
      "\n",
      "y = np.array(x.size, dtype=np.double)\n",
      "y.resize(x.size)\n",
      "for i in range(0, y.size):\n",
      "    y[i] = fi2.f(x[i])\n",
      "\n",
      "fig, axes = plt.subplots(figsize=(10,6), dpi=100)\n",
      "axes.plot(t, y, 'r')\n",
      "axes.plot(t, x)\n",
      "axes.set_xlabel('Time (s)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 68,
       "text": [
        "<matplotlib.text.Text at 0x7f40b82e4a58>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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kqZHBKgWDlSRJamSwSqGQVYEGK0mSSqudYLUEWA2sAa6a5JhB4AngGWA4RmHdwI6VJElq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\nJEmSJEmSJEmSJEmSJEmS1J7/D3fX0KOwLllLAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f40b846a320>"
       ]
      }
     ],
     "prompt_number": 68
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Impulse response"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = pylab.hstack([pylab.zeros(tau), 1, pylab.zeros(9*tau - 1)])\n",
      "t = pylab.linspace(0, tau / 10, x.size)\n",
      "fi2 = iir.Filter(fi)\n",
      "\n",
      "y = np.array(x.size, dtype=np.double)\n",
      "y.resize(x.size)\n",
      "for i in range(0, y.size):\n",
      "    y[i] = fi2.f(x[i])\n",
      "\n",
      "fig, axes = plt.subplots(figsize=(10,6), dpi=100)\n",
      "axes.plot(t, y, 'r')\n",
      "axes.plot(t, x)\n",
      "axes.set_xlabel('Time (s)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 69,
       "text": [
        "<matplotlib.text.Text at 0x7f40b83cce80>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bQzPX4WhgLvDRSGNRcxq5dpcTbv1SJvweTHMPP2Wrkes3EfggcAywLaHq/DBh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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f40b83edf28>"
       ]
      }
     ],
     "prompt_number": 69
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Linear Bode plot"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "freq = pylab.linspace(0, nyquist_freq, num_points)\n",
      "resp = respfunc(freq)\n",
      "\n",
      "fig, axes = plt.subplots(nrows=2, ncols=1, figsize=(10, 10), dpi=100)\n",
      "\n",
      "axes[0].plot(freq, abs(resp), 'r')\n",
      "axes[0].set_xlabel('Frequency (Hz)')\n",
      "axes[0].set_ylabel('Magnitude')\n",
      "\n",
      "axes[1].plot(freq, pylab.angle(resp), 'r')\n",
      "axes[1].set_xlabel('Frequency (Hz)')\n",
      "axes[1].set_ylabel('Phase (radians)')\n",
      "axes[1].set_ylim([-pylab.pi, pylab.pi])\n",
      "axes[1].set_yticks(pylab.linspace(-pylab.pi, pylab.pi, 9))\n",
      "axes[1].set_yticklabels([\"-\u03c0\", \"-\u00be\u03c0\", \"-\u00bd\u03c0\", \"-\u00bc\u03c0\", \"0\", \"\u00bc\u03c0\", \"\u00bd\u03c0\", \"\u00be\u03c0\", \"\u03c0\"])\n",
      "\n",
      "None"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1715y+d0lW33DWT7HCZoCNwD7ArOAMcDjwMcZzzkA6AH0BAYANwED81ij8sD/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\nSZKktPl/h3fA+OvbGmoAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f40b83d4390>"
       ]
      }
     ],
     "prompt_number": 70
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Logarithmic Bode plot"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "freq = pylab.logspace(-3, pylab.log10(nyquist_freq), num_points)\n",
      "resp = respfunc(freq)\n",
      "\n",
      "fig, axes = plt.subplots(nrows=2, ncols=1, figsize=(10, 10), dpi=100)\n",
      "\n",
      "axes[0].plot(freq, 10 * pylab.log10(abs(resp)), 'r')\n",
      "axes[0].set_xlabel('Frequency (Hz)')\n",
      "axes[0].set_xscale('log')\n",
      "axes[0].set_ylabel('Magnitude (dB)')\n",
      "axes[0].axhline(y=-3)\n",
      "for f in halfgain:\n",
      "    axes[0].axvline(f)\n",
      "\n",
      "axes[1].plot(freq, pylab.angle(resp), 'r')\n",
      "axes[1].set_xlabel('Frequency (Hz)')\n",
      "axes[1].set_xscale('log')\n",
      "axes[1].set_ylabel('Phase (radians)')\n",
      "axes[1].set_ylim([-pylab.pi, pylab.pi])\n",
      "axes[1].set_yticks(pylab.linspace(-pylab.pi, pylab.pi, 9))\n",
      "axes[1].set_yticklabels([\"-\u03c0\", \"-\u00be\u03c0\", \"-\u00bd\u03c0\", \"-\u00bc\u03c0\", \"0\", \"\u00bc\u03c0\", \"\u00bd\u03c0\", \"\u00be\u03c0\", \"\u03c0\"])\n",
      "\n",
      "None"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+52pTA4XdvxPowO+8LuWLLzL5TQAAMwkrQOR7OLup9hRy/y7BSaBrVSH370Na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\nkiRJkiRJkiRJkiRJkiRJyp7/Af4lzyISHNnnAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f40b8467b70>"
       ]
      }
     ],
     "prompt_number": 71
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 71
    }
   ],
   "metadata": {}
  }
 ]
}