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pythonnumpyscipyconvolution

Python: 1d array circular convolution

I wonder if there's a function in numpy/scipy for 1d array circular convolution. The scipy.signal.convolve() function only provides "mode" but not "boundary", while the signal.convolve2d() function needs 2d array as input.

I need to do this to compare open vs circular convolution as part of a time series homework.

Solution

  • Since this is for homework, I'm leaving out a few details.

    By the definition of convolution, if you append a signal a to itself, then the convolution between aa and b will contain inside the cyclic convolution of a and b.

    E.g., consider the following:

    import numpy as np
from scipy import signal

%pylab inline

a = np.array([1] * 10)
b = np.array([1] * 10)

plot(signal.convolve(a, b));

    enter image description here

    That is the standard convolution. Now this, however

    plot(signal.convolve(a, np.concatenate((b, b))));

    enter image description here

    In this last figure, try to see where is the result of the circular convolution, and how to generalize this.