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pythonnumpyfft
CD86
CD86

Reputation: 1079

numpy fftn order of individual ffts

fft2 and fftn provide the axis parameter which allows to specify over which axes to perform the transform. Does the method obey order?

Given a 2-dimensional numpy array

a = np.array([[1,2],[3,4]])

is

fft2(a,axis=(0,1)

different from 

fft2(a,axis=(1,0)

I have data which is correlated across lines but not columns...

Upvotes: 0

Views: 244

Answers (1)

Nils Werner
Nils Werner

Reputation: 36765

The DFT is separable, which means calculating the 2D DFT is the same as calculating two individual 1D DFTs along each axis:

import numpy as np

a = np.arange(25).reshape(5, 5)

out1 = np.fft.fft2(a)

tmp = np.fft.fft(a, axis=0)
out2 = np.fft.fft(tmp, axis=1)

np.allclose(out1, out2) # True

And since the nested summations of the DFTs commute, the order of operations does not matter

tmp = np.fft.fft(a, axis=1)
out3 = np.fft.fft(tmp, axis=0)

np.allclose(out1, out3) # True

Which means the order of the axes parameter does not matter either

out4 = np.fft.fft2(a, axes=(1, 0))

np.allclose(out1, out4) # True

Upvotes: 4

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