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Why am I getting this strange figure? I understand that the peak is when I am most correlated. So its saying I am most correlated without shifting my data, but why isn't it normalized?

I want to be able to take data like this and produce a measurement of how similar they are. They're from the same hardware under different conditions, so they essentially have the same shape, but may differ in magnitude, or shape of their rough 'peaks'. enter image description here enter image description here

import matplotlib.pyplot as plt
import numpy as np

a = np.array([0, 80, 83, 86, 85, 82, 84, 85, 86, 85, 87, 84, 85, 88, 89, 88, 87, 88, 86, 87, 88, 85, 86, 84, 83, 85, 83, 82, 84, 83, 81, 83, 80, 82, 83, 81, 79, 80])
b = np.array([0, 81, 82, 85, 86, 81, 85, 84, 87, 84, 88, 83, 86, 89, 88, 87, 88, 87, 87, 86, 89, 86, 85, 83, 84, 86, 84, 81, 83, 84, 82, 84, 81, 83, 82, 82, 80, 79])

a=a/a.std()
b=b/b.std()


plt.plot(a)
plt.plot(b)

xcorr = np.correlate(a,b,'full')/len(a)
plt.plot(xcorr)
Clay Chester
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  • What have you tried for your own debugging? For example: "What is the orange line?" Try commenting out the `plt.plot(xcorr)` line and see that the orange line as actually the two lines you plotted for `a` and `b` – G. Anderson Feb 19 '21 at 18:08
  • See [Python debugging tips](https://stackoverflow.com/questions/1623039/python-debugging-tips) – G. Anderson Feb 19 '21 at 18:09

1 Answers1

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The cross correlation is already telling you how similar they are, only that the similarity is expressed in the metric of the original signals so there's no reason to expect the resulting correlations to be normalized or constrained between 0-1

If you want to normalize the resulting correlation (like in MATLAB, for example), you could try scaling the values by the product of their norms:

a = np.array([0, 80, 83, 86, 85, 82, 84, 85, 86, 85, 87, 84, 85, 88, 89, 88, 87, 88, 86, 87, 88, 85, 86, 84, 83, 85, 83, 82, 84, 83, 81, 83, 80, 82, 83, 81, 79, 80])
b = np.array([0, 81, 82, 85, 86, 81, 85, 84, 87, 84, 88, 83, 86, 89, 88, 87, 88, 87, 87, 86, 89, 86, 85, 83, 84, 86, 84, 81, 83, 84, 82, 84, 81, 83, 82, 82, 80, 79])

xcorr = np.correlate(a,b,'full') / (np.linalg.norm(a) * np.linalg.norm(b))
plt.plot(xcorr)

enter image description here

As for why it looks like a triangle, that is due to the way a cross correlation is calculated. You are essentially calculating a correlation at every single time step - imagine sliding one signal over the other. You do this with both the positive lag values (which give you the correlations after your peak), as well as the negative lags (which give you the values before the peak). Your 0-lag correlation will be the peak in the middle.

Also, if you print your cross correlation values, you'll notice that the values aren't actually perfectly symmetrical, it only looks that way in the figure due to the similarity of your 2 signals:

[0.         0.02400722 0.0492186  0.07594942 0.10241434 0.12830187
 0.1541742  0.1812317  0.20800811 0.2351112  0.26253336 0.28842089
 0.31552398 0.34409333 0.37248414 0.40026338 0.42832372 0.45693105
 0.48596003 0.51442302 0.54342921 0.57155412 0.60023743 0.62805465
 0.65586048 0.68463116 0.7118596  0.7378231  0.76583785 0.79238634
 0.81931089 0.84595435 0.87183428 0.89713682 0.92421712 0.95038574
 0.9751033  0.99993102 0.97567309 0.95038574 0.92356755 0.89708744
 0.87113913 0.84522121 0.81801557 0.79107962 0.76396894 0.7364518
 0.71045791 0.68327505 0.65454616 0.62608697 0.59827735 0.57016003
 0.54142354 0.51244774 0.48403794 0.45500136 0.42702839 0.3982881
 0.37053925 0.34283979 0.31426664 0.28709518 0.26126083 0.23321189
 0.20673178 0.18000475 0.15355503 0.1276599  0.10241054 0.07536063
 0.04922619 0.024615   0.        ]
Simon
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