2D FFT of a 4D matrix

Hi,

I have a 4D matrix M(x,px,y,py); I need to perform 2D FFT along the (x,y) coordinates and a 2DIFFT along the (px,py) coordinates. Is it possible to use only FFT ( and IFFT) function which can deal with separated dimensions ? Or maybe FFT2 (and IFFT2) although this function cannot work along specific dimensions ? Thank you for any help.

Answer 1

[Bjorn Gustavsson]

Shouldn't this effectively be the same as running an FFT on the entire 4D-array (with some confusion about normalization-factors)?

[Roger ALIMI]

Thank you Bjorn for your suggestion,

Given M being the 4Dmatrix of size (Nx,Npx,Ny,Npy), I am pretty sure that it should be equivalent to

A = fft(fft(fft(M),Npx,2)) ;

B = fft(fft(fft(A),Npy,4)) ;

C = ifft(ifft(ifft(B),Nx,1)) ;

D = ifft(ifft(ifft(C),Ny,3)) ;

with some normalizations on the way. But how can I check the result ?

[Bjorn Gustavsson]

Well you have the convenient fftn function that lets you do them in one call.

Ft_allatonce = fftn(M);

To check the results you might "simply" (it is never as "simply" as I like to think...) compare a couple of different slices of that with what you get from a nested call like this:

Ft_OnebyOne = ifft(ifft(fft(fft(M,[],1),[],3),[],2),[],4);

HTH

[Roger ALIMI]

Thanks again Bjorn,

FFTN is not an option since I need to perform FFT on 2 dimensions and IFFT on the others, and neither FFTN nor IFFTN does not allow to choose the dim along which you want to perform the transform.

[Bjorn Gustavsson]

What difference between an fft and an ifft do you worry about?

[Roger ALIMI]

Hi Bjorn,

I cannot apply fftn at once because it has to work on 2 dimensions only. The other 2 dims are to be inverse transformed. And fftn does not allow chosing a specific dimension. Anyway thank you for your remarks.

Roger

[Bjorn Gustavsson]

Yes, I get that. However, the fft and ifft only differ with respect to the sign of the complex exponent and a scaling-factor of 1/N. The 1/N scaling-factor is, surely, a nonsense issue for you. Why would it be prohibitive for you to take the change of the phase-angle components into account? If those are really a stop-issue my second sequence of wrapped calls should be what you're after.

HTH

[Roger ALIMI]

Thanks again Bjorn,

You are right, using a sequential call of 2 ffts and 2 iffts (the order does does not matter I guess) seems to do the job.

Regards,

Roger

[Bjorn Gustavsson]

Great that it solved your problem.

The order should by definition not matter since the transform separates over orthogonal dimensions...