signal-processing/lti.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "from http://www.shocksolution.com/2010/12/linear-system-simulation-with-python/"
   ]
  },
  {
   "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": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/scipy/signal/ltisys.py:554: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  GT = dot(dot(vti, diag(numpy.exp(dt * lam))), vt).astype(xout.dtype)\n",
      "/usr/lib/python3/dist-packages/scipy/signal/ltisys.py:568: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  vt).astype(xout.dtype)\n"
     ]
    },
    {
     "data": {
      "image/png": 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YmBgcOHCgw2Mx7ImI5GE17M1mMxYsWICCggKUlJQgJycHx44da7VPXl4eTp48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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0eea8b77d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import signal\n",
    "\n",
    "tau = 5.0 * 60  # 5 minutes\n",
    "h_times = arange(0.0, 10 * tau, 0.1)\n",
    "\n",
    "sys = signal.lti(1, [1, 1.0 / tau])\n",
    "\n",
    "step_response = sys.step(T=h_times)[1]\n",
    "plot(h_times, step_response / step_response.max())  # normalized\n",
    "axhline(0.63, color='red')\n",
    "axvline(tau, color='red')\n",
    "xlabel('t')\n",
    "title('Step response')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`scipy.signal.iirdesign()` -> http://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.iirdesign.html#scipy.signal.iirdesign\n",
    "\n",
    "`scipy.signal.lfilter()` -> http://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.lfilter.html#scipy.signal.lfilter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p xmlns:dct=\"http://purl.org/dc/terms/\">\n",
    "  <a rel=\"license\"\n",
    "     href=\"http://creativecommons.org/publicdomain/zero/1.0/\">\n",
    "    <img src=\"http://i.creativecommons.org/p/zero/1.0/88x31.png\" style=\"border-style: none;\" alt=\"CC0\" />\n",
    "  </a>\n",
    "  <br />\n",
    "  To the extent possible under law,\n",
    "  <span rel=\"dct:publisher\" resource=\"[_:publisher]\">the person who associated CC0</span>\n",
    "  with this work has waived all copyright and related or neighboring\n",
    "  rights to this work.\n",
    "</p>"
   ]
  }
 ],
 "metadata": {
  "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": "3.4.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}