CODEWITHSUNDEEP
pythonnumpyscipycorrelation
Sebastiano1991
Sebastiano1991

Reputation: 897

signal.correlate 'same'/'full' meaning?

I am wondering what the mode arguments in signal.correlate (or numpy.correlate) mean? 

def crossCorrelator(sig1, sig2):
    correlate = signal.correlate(sig1,sig2,mode='same')
    return(correlate)
flux0 = [ 0.02006948  0.01358697 -0.06196026 -0.03842506 -0.09023056 -0.05464169 -0.02530553 -0.01937054 -0.01237411  0.03472263  0.17865012  0.27441767  0.23532932  0.16358341  0.08743969  0.12166425  0.10287468  0.13430794  0.08262321  0.0515434   0.04657624  0.09017276  0.09131331  0.04696824 -0.03901519 -0.01413654  0.05448175  0.1236946   0.09968044 -0.001584 -0.06094561 -0.02998289 -0.00113092  0.04336605  0.01105071  0.0527657  0.03825847  0.02309524]

flux1 = [-0.02946104 -0.02590192 -0.02274955  0.00485888 -0.0149776   0.01757462  0.02820086  0.0379213   0.03580811  0.06507382  0.09995243  0.12814133  0.16109725  0.12371425  0.08273643  0.09433014  0.05137761  0.04057405 -0.08171598 -0.06541216  0.00126869  0.09223577  0.06811737  0.0795967  0.08689563  0.0928949   0.09971169  0.05413958  0.05410236  0.00120439  0.02454734  0.06450544  0.01508899 -0.06100537 -0.10038889 -0.00651572  0.01095773  0.05517478]

correlation = crossCorrelator(flux0,flux1)

f, axarr = plt.subplots(2)
axarr[0].plot(np.arange(len(flux0)),flux0)
axarr[0].plot(np.arange(len(flux1)),flux1)
axarr[1].plot(np.arange(len(correlation)),correlation)
plt.show()

When I use mode 'same' the correlation array has same dimension as the fluxes for full it has double? If the len(flux0/1) is of dimension time what dimension would len(correlation) be ?

I am really more looking for a mathematical explanation, the answers I have found so far were more of technical nature...

Upvotes: 2

Views: 2312

Answers (1)

user8153
user8153

Reputation: 4095

Given two sequences (a[0], .., a[A-1]) and (b[0], .., b[B-1]) of lengths A and B, respectively, the convolution is calculated as

c[n] = sum_m a[m] * b[n-m]

If mode=="full" then the convolution is calculated for n ranging from 0 to A+B-2, so the return array has A+B-1 elements.

If mode=="same" then scipy.signal.correlate computes the convolution for n ranging from (B-1)/2 to A-1+(B-1)/2, where integer division is assumed. The return array has A elements. numpy.correlate behaves the same way only if A>=B; if A is less than B it switches the two arrays (and the returned array has B elements).

If mode=="valid" then the convolution is calculated for n ranging from min(A,B)-1 to max(A,B)-1, and therefore has max(A,B)-min(A,B)+1 elements.

Upvotes: 2

Related Questions