176 lines
59 KiB
Plaintext
176 lines
59 KiB
Plaintext
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{
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"metadata": {
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"name": "",
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"signature": "sha256:5b0dafe7d37bc894511c97dd35f5e879105d8ec76b5947ed751b794510920348"
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},
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"nbformat": 3,
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"nbformat_minor": 0,
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"worksheets": [
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{
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"cells": [
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{
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"cell_type": "heading",
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"level": 1,
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"metadata": {},
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"source": [
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"Filter analysis test"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"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."
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"import iir\n",
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"\n",
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"# change this to alter the sample rate we are displaying at\n",
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"sample_rate = 100 # Hz\n",
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"nyquist_freq = sample_rate / 2\n",
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"\n",
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"# build the filter object, fi, here\n",
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"corner_freq = 10 # Hz\n",
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"order = 4\n",
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"fi = iir.Filter(\"butterworth_lowpass(%d, 1.0, %f)\" % (order, corner_freq / nyquist_freq))"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 69
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Here we set up the plotting library and helper functions."
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"%matplotlib inline\n",
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"import matplotlib.pyplot as plt\n",
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"import pylab\n",
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"\n",
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"# number of points to plot on graphs (arbitrary)\n",
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"num_points = 1000\n",
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"\n",
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"# helper function: calls the Filter.response() method on each member of the array\n",
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"respfunc = pylab.vectorize(lambda f: fi.response(f/sample_rate))"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 70
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},
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{
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"cell_type": "heading",
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"level": 2,
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"metadata": {},
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"source": [
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"Linear Bode plot"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"freq = pylab.linspace(0, nyquist_freq, num_points)\n",
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"resp = respfunc(freq)\n",
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"\n",
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"fig, axes = plt.subplots(nrows=2, ncols=1, figsize=(10, 10), dpi=100)\n",
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"\n",
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"axes[0].plot(freq, abs(resp), 'r')\n",
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"axes[0].set_xlabel('Frequency (Hz)')\n",
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"axes[0].set_ylabel('Magnitude')\n",
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"\n",
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"axes[1].plot(freq, angle(resp), 'r')\n",
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"axes[1].set_xlabel('Frequency (Hz)')\n",
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"axes[1].set_ylabel('Phase (radians)')\n",
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"axes[1].set_ylim([-pi, pi])\n",
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"axes[1].set_yticks(linspace(-pi, pi, 9))\n",
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"axes[1].set_yticklabels([\"-\u03c0\", \"-\u00be\u03c0\", \"-\u00bd\u03c0\", \"-\u00bc\u03c0\", \"0\", \"\u00bc\u03c0\", \"\u00bd\u03c0\", \"\u00be\u03c0\", \"\u03c0\"])\n",
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"\n",
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"None"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"metadata": {},
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"output_type": "display_data",
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"png": "iVBORw0KGgoAAAANSUhEUgAAAmcAAAJeCAYAAADxx6J0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAh6v9pzHgEGEyQNtgAHARw2o
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"text": [
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"<matplotlib.figure.Figure at 0x7fce9ce81e80>"
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]
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}
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],
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"prompt_number": 71
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},
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{
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"cell_type": "heading",
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"level": 2,
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"metadata": {},
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"source": [
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"Logarithmic Bode plot"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"freq = pylab.logspace(-3, log10(nyquist_freq), num_points)\n",
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"resp = respfunc(freq)\n",
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"\n",
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"fig, axes = plt.subplots(nrows=2, ncols=1, figsize=(10, 10), dpi=100)\n",
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"\n",
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"axes[0].plot(freq, 10 * log10(abs(resp)), 'r')\n",
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"axes[0].set_xlabel('Frequency (Hz)')\n",
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"axes[0].set_xscale('log')\n",
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"axes[0].set_ylabel('Magnitude (dB)')\n",
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"axes[0].axhline(y=-3)\n",
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"\n",
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"axes[1].plot(freq, angle(resp), 'r')\n",
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"axes[1].set_xlabel('Frequency (Hz)')\n",
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"axes[1].set_xscale('log')\n",
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"axes[1].set_ylabel('Phase (radians)')\n",
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"axes[1].set_ylim([-pi, pi])\n",
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"axes[1].set_yticks(linspace(-pi, pi, 9))\n",
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"axes[1].set_yticklabels([\"-\u03c0\", \"-\u00be\u03c0\", \"-\u00bd\u03c0\", \"-\u00bc\u03c0\", \"0\", \"\u00bc\u03c0\", \"\u00bd\u03c0\", \"\u00be\u03c0\", \"\u03c0\"])\n",
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"\n",
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"None"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"metadata": {},
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"output_type": "display_data",
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||
|
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"text": [
|
||
|
|
"<matplotlib.figure.Figure at 0x7fce9d421ac8>"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"prompt_number": 72
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"collapsed": false,
|
||
|
|
"input": [],
|
||
|
|
"language": "python",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"prompt_number": 34
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {}
|
||
|
|
}
|
||
|
|
]
|
||
|
|
}
|