libfir/python/filter_analysis.ipynb

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Plaintext

{
"metadata": {
"name": "",
"signature": "sha256:05ffaa60d7b0775a690325e7dd783d1e09e0b0e286dd523bfcba985a0ea7cfe0"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import fir\n",
"\n",
"sample_rate = 20 # Hz\n",
"corner = 1.6 # Hz\n",
"gain = 1.0\n",
"npoints = 501\n",
"\n",
"nyquist_freq = sample_rate / 2\n",
"\n",
"fi = fir.BlackmanLowpass(npoints, corner / sample_rate, gain)\n",
"\n",
"# this code will read points from an ASCII file, one point per line\n",
"#points = []\n",
"#f = open(\"div5.txt\", \"r\")\n",
"#for line in f:\n",
"# points.append(float(line))\n",
"#npoints = len(points)\n",
"#fi = fir.Filter(points)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 106
},
{
"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": 107
},
{
"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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2aVlTCCGEmICcpzVvDDwbuC1N9utXge8Du4CPJex/V5qHCC6g+czTW4AHOsr9CfC2ed1i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lo7lKFq7MW7FpLzoMAeaJNh4sbXUucaIOH69gSI3GlL4ylliJZd0DFzdVrcjveul8TUI8Ezsj81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\nm1Y/jkH6awAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7fec43a14d30>"
]
}
],
"prompt_number": 108
},
{
"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": 109,
"text": [
"[<matplotlib.lines.Line2D at 0x7fec4383ba90>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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TOe64uPVcPv7xRNCXL68clQnGsrMX2447GssxZKmHsP7OtPwrliVLKsMfs7Bi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\nQgghhFhD+X8J1kPD/YdrfwAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7fec43bff668>"
]
}
],
"prompt_number": 109
},
{
"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, 20 * 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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1UpATEREZqbZsgYcegnnzYP78wa9nnjHr2R18sAl2BxxglkGZMQMmTKisuQpy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GLX1IG1uj7dJIoDALwOwCnLj4Fgrb62ctzJQ9+K3He/G8hGzj6ardGKwP7whyHzpytCPA2KXBfJ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\nSZIkSZIkSZIkSc3nP1ygQaomewRVAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x7fec4382dcc0>"
]
}
],
"prompt_number": 110
},
{
"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": 111,
"text": [
"<matplotlib.text.Text at 0x7fec436b6860>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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ACHRbe9RZgTAZZG3kskjqp3r70T6StC1tj7cq0v5g92nA7cATwFLgTOBfCDOp\nz6A9PB0JlAiPhnqYrh8Y/2nCkxtayuvfIDy2Yw5hVn8ID6V9hvCoE0naYQYuSX3VPsAJhO6+XwCP\nAocQHol1GqE16nrgS8AngduAH3RxnmMJgazN1cBhhEd5XFqx/TnguB79BJJyY2tN6JK0s0oILVlb\nCM98qwIeKe+bS3jI+QHAxwjPOgOoJjyDsrOPAk9WrL8M3El4EG3lw2hXEp7NKEk7zMAlqa9qKv9s\nBZortrcSfrcVCF2Dx2zHuQoVy6cRWrK+AHwH+Hj5nFWEoCdJO8wuRUl9UWHbh7AA2AM4qrxeC0zs\n4rhltI/tKhBavErANcAIYFh5317lYyVphxm4JO3skoqfXS3DB1ueEkKr11nAPxHuMJwFHN3F+Z8k\njPGC0DJ2B6Fb8SXgfwPvlPdNIgzSlyRJ0g5qmxZiwFaOqSKENodhSPpQqnu7AJK0E6gGDiaEqq58\nAXiL0NUoSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSeof/j+/5f2NMZOESwAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7fec438d1cc0>"
]
}
],
"prompt_number": 111
},
{
"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": 112,
"text": [
"<matplotlib.text.Text at 0x7fec437bf240>"
]
},
{
"metadata": {},
"output_type": "display_data",
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"text": [
"<matplotlib.figure.Figure at 0x7fec439d7c88>"
]
}
],
"prompt_number": 112
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 112
}
],
"metadata": {}
}
]
}