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@pierre-haessig
Last active July 2, 2018 13:28
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{
"metadata": {
"name": "",
"signature": "sha256:d6ce0ba3b9204d6ab22f8f00a2a5c6bf11d28ddd8c6154c9c7122536fcb704df"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<H1> Correlation of discrete signals </H1>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%pylab\n",
"%matplotlib inline"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Using matplotlib backend: Qt4Agg\n",
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Correlation is a measurement of how similar two signals. The <B>cross correlation</B> allows us to measure the similiarity between two signals at different lag positions."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Sin function to generate signals\n",
"\n",
"delay = 0.6 # ms\n",
"\n",
"f = lambda(x) : np.sin(x) # original signal\n",
"g = lambda(x) : np.sin(x - delay)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 34
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"dt = 0.05 # sampling interval (in ms)\n",
"time = np.arange(start = 0, stop = 30.00, step = dt) # sample 30 ms seconds at 20 kHz (100 samples)\n",
"\n",
"# generate signals\n",
"A, B = f(time), g(time)\n",
"\n",
"# Plot signals\n",
"plt.plot(time, A, lw=1, color = 'magenta');\n",
"plt.plot(time, B, lw=1, color = 'blue');\n",
"plt.xlabel('Time (ms)');\n",
"plt.ylabel('Signal (AU)');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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NG4XFQxEi6HPnWizotcRdIdsW4yaUG7uegRGo2C1GlhWjhjC6Cpv8Y8eG/N/ZSGhXEaq0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\n",
"text": [
"<matplotlib.figure.Figure at 0xaf1d862c>"
]
}
],
"prompt_number": 35
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# compute signal autocorrelation\n",
"\n",
"coor = np.correlate(A, A, 'full')\n",
"maxlag = coor.size/2\n",
"\n",
"lag = np.arange(-maxlag, maxlag+1)*dt\n",
"\n",
"plt.plot(lag, coor, lw=1);\n",
"line = plt.axvline(x=0, ymin=-40, ymax = 50, linewidth=1.5, color='r')\n",
"line.set_dashes([8, 4, 2, 4, 2, 4]) "
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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L2qfXlofJtGsnCz9nzfL/HhDc/eMweHDwstCO/99ra79UTFgATgA46FhMxAAO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\n",
"text": [
"<matplotlib.figure.Figure at 0xaf2caf0c>"
]
}
],
"prompt_number": 36
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# compute cross correlation\n",
"\n",
"coor = np.correlate(A, B, 'full')\n",
"maxlag = (coor.size-1)/2 \n",
"lag = np.arange(-maxlag, maxlag+1)*dt\n",
"\n",
"# plot cross correlogram with line about 1 ms\n",
"plt.plot(lag, coor, lw=1);\n",
"line = plt.axvline(x=-delay, ymin=np.min(coor), ymax = np.max(coor), linewidth=1.5, color='c')\n",
"line.set_dashes([8, 4, 2, 4, 2, 4])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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69VLGZuzYagYOnM9nPjOf5cvne/6dxWgJWQ+MTHs9ErEC2nDgwHz+/GdpqrBj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\nKIqiKIqiKIqiKIqiKIoC8P8BXKEqAsn75WAAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0xaefc1eac>"
]
}
],
"prompt_number": 37
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Calculate lag position of maximal correlation\n",
"def lag_ix(x,y):\n",
"\n",
" corr = np.correlate(x,y,mode='full')\n",
" pos_ix = np.argmax( np.abs(corr) )\n",
" lag_ix = pos_ix - (corr.size-1)/2\n",
" return lag_ix\n",
"\n",
"lag_ix(A,B)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 38,
"text": [
"-11"
]
}
],
"prompt_number": 38
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"delay_estimation = -lag_ix(A,B)*dt\n",
"delay_estimation"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 44,
"text": [
"0.55000000000000004"
]
}
],
"prompt_number": 44
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(lag, coor, lw=1);\n",
"line = plt.axvline(x=-delay_estimation, ymin=-40, ymax = 50,\n",
" linewidth=1.5, color='r', label='estimated delay')\n",
"line = plt.axvline(x=-delay, ymin=np.min(coor), ymax = np.max(coor),\n",
" linewidth=1.5, color='c', label='true delay')\n",
"\n",
"line.set_dashes([8, 4, 2, 4, 2, 4]) \n",
"plt.xlim(-2*delay, 0)\n",
"\n",
"plt.legend(loc='lower right');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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QSiDYBeTXMn0isAwoBwqAPcBwoAfQCdhoL/cGMCmE7YuISBg0xzmCNOCg3+uDQHot0wvt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\n",
"text": [
"<matplotlib.figure.Figure at 0xaf20b2ac>"
]
}
],
"prompt_number": 48
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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