How to take fft along a specific direction?

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Jamie Al
Jamie Al 2022-3-31
评论： Bjorn Gustavsson 2022-4-11
I have this function that's periodic in x but non-periodic in y and I was able to perform fft along the periodic direction in the following way:
ubar = Y.^2 .* sin( (2*pi / Lx) * X);
uh = fft(ubar,[],2); %fft over periodic direction
duhdxk = derivk(uh, kx);
duhdx = real(ifft(duhdxk,[],2));
This works fine as I can check the derivative along x and it gives correct results.
now I am trying to do the same thing for a 3D function instead where x and y are periodic and z is non-periodic but for some reason I keep getting wrong results, what I did was:
ubar = Z.^2 .* sin( (2*pi / Lx) * X) .* sin( (2*pi / Ly) * Y) ;
uh = fft(fft(ubar,[],2),[],3); %fft over periodic direction X and Y
duhdxk = derivk(uh, kx);
duhdx = real(ifft(ifft(ubar,[],2),[],3));
This is not working, can someone tell me how to take fft along x and y but not z?

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Bjorn Gustavsson
Bjorn Gustavsson 2022-4-1
Perhaps it is a simple as:
uh = fft(fft(ubar,[],1),[],2); %fft over periodic direction X and Y
Since to my understanding the X, and Y coordinates typically vary along the second and first dimensions (if generated by meshgrid) or the first and second dimensions (if generated by ndgrid). (Unless you have manually selected to have Z vary along the first dimensin).
HTH
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Bjorn Gustavsson
Bjorn Gustavsson 2022-4-2
Then my suggestion should leave you with the x-y-Fourier-transformed 3-D array with the FT on each Z-slice such that you can look at the amplitudes of the 12th slice:
imagesc(fftshift(log10(abs(uh(:,:,12))))) % fftshift to centre the DC-component
or look at the Z-variation of the X-Fourier-coefficients for some wavenumber in Y:
imagesc(log10(abs(squeeze(uh(12,:,:))))) % not fftshifted
HTH

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