2D DFFT: wrong order along the second dimension

Specific Domains Numerics
1

Let us consider a 2D discrete fast Fourier transform of a separable function:

using FFTW
xs = collect(0.0:0.1:0.9)
ys = xs
zs = cos.(xs).^2*sin.(ys')
fzs = fft(zs)

The result of 2D DFF transform of zs is

fzs
fzs1654×325 34 KB

On the other hand, since the function is separable, we can compute 2D Fourier transform as a product of two 1D Fourier transforms:

fzs2 = fft(cos.(xs).^2)*fft(sin.(ys))'

This gives us

fzs2
fzs21653×324 33.9 KB

As we see, the two results do not exactly coincide. However, if we permute the columns of fzs2, we actually obtain fzs: we need to permute columns 2 and 10, 3 and 9, etc. If one does fft shift, it corresponds to exchanging columns corresponding to ky and -ky.

Can anyone explain why this happens?

2

you need transpose(fft(sin.(ys))), what you are doing is the adjoint which is the transpose, complex conjugated. You don’t see the effect on ys since it was real.

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