libfir/python/filter_analysis.ipynb

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149 KiB
Plaintext

{
"metadata": {
"name": "",
"signature": "sha256:059af54bd0e19f56f028eec31f2ad301153d3f7d6d47b7b235667783d0bcff25"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import fir\n",
"\n",
"sample_rate = 1000 # Hz\n",
"corner = 100 # Hz\n",
"gain = 1.0\n",
"npoints = 501\n",
"\n",
"nyquist_freq = sample_rate / 2\n",
"\n",
"fi = fir.LanczosLowpass(npoints, corner / sample_rate, gain, 3)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 44
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import pylab\n",
"\n",
"bode_points = 997 # non-multiple number avoids numeric effects/beating\n",
"respfunc = pylab.vectorize(lambda f: fi.response(f/sample_rate))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 45
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Linear Bode plot"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"freq = pylab.linspace(0, nyquist_freq, bode_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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t1z3ua/x+CDgTc3/zvmu/mAvmSmeYxfjJBEl//GcYP6ByMvBsTPvqxo/1GQD+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ezELFHUtPcl8We5+qXymcSuT8gfPGwwGAwGwwyi30StSYyat0mpZTt2wM6do/FnoY18Xmgbtazp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\n",
"text": [
"<matplotlib.figure.Figure at 0x7f77ae68c0b8>"
]
}
],
"prompt_number": 50
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Group delay"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ph = pylab.angle(resp)\n",
"\n",
"# heuristic \"de-modulo\" operation\n",
"for i in range(1,ph.size):\n",
" phdiff = ph[i - 1] - ph[i]\n",
" if(phdiff > pylab.pi):\n",
" ph[i:ph.size] += pylab.pi\n",
" elif(phdiff < pylab.pi):\n",
" ph[i:ph.size] -= pylab.pi\n",
"\n",
"ph /= -freq * 2 * pylab.pi\n",
"\n",
"plt.plot(freq, ph)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 52,
"text": [
"[<matplotlib.lines.Line2D at 0x7f77ae6743c8>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
"<matplotlib.figure.Figure at 0x7f77aea80400>"
]
}
],
"prompt_number": 52
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Logarithmic Bode plot"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"freq = pylab.logspace(-1, pylab.log10(nyquist_freq), bode_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",
"\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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xoqqIiEijsdNpRMms3XqrmUQ2Lvv8gQN7doOefrpZTsp9Pfu4XVnAa0yZX2Zt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\ngg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7f77ae66c4e0>"
]
}
],
"prompt_number": 40
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Impulse response"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fi2 = fir.Filter(fi)\n",
"acausal = int(npoints / 2)\n",
"steady = 10\n",
"x = pylab.hstack([pylab.zeros(npoints + steady), 1, pylab.zeros(npoints + steady)])\n",
"t = pylab.linspace(0, x.size/sample_rate, x.size)\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, x)\n",
"axes.plot(t - acausal/sample_rate, y, 'r')\n",
"axes.set_xlabel('Time (s)')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 34,
"text": [
"<matplotlib.text.Text at 0x7f77ae067588>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
"<matplotlib.figure.Figure at 0x7f77ae5d6b00>"
]
}
],
"prompt_number": 34
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Step response"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fi2 = fir.Filter(fi)\n",
"acausal = int(npoints / 2)\n",
"steady = 10\n",
"x = pylab.hstack([pylab.zeros(npoints + steady), 1, pylab.ones(npoints + steady)])\n",
"t = pylab.linspace(0, x.size/sample_rate, x.size)\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, x)\n",
"axes.plot(t - acausal/sample_rate, y, 'r')\n",
"axes.set_xlabel('Time (s)')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 35,
"text": [
"<matplotlib.text.Text at 0x7f77ae5b4470>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
"<matplotlib.figure.Figure at 0x7f77ae3af588>"
]
}
],
"prompt_number": 35
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 35
}
],
"metadata": {}
}
]
}