I would like to rewrite fftshift(f​ft2(fftshi​ft(x)))) as F*x*F.' but how do I handle the fftshifts?

I would like to rewrite fftshift(fft2(fftshift(x)))) as F*x*F.' (where F = dftmtx(N) and N is the size of x), but how do I handle the fftshifts?

Thanks so much for your help!

Christine

Answer 1

[Matt J]

    F=fft(  fftshift(eye(N),1)  ,[],1);
    F=fftshift(F,1);

[Matt J]

Or, if you have the Signal Processing Toolbox,

    A=fftshift(speye(N),1);
    F=A*dftmtx(N)*A;

[SwishSwisher]

Thanks again! you rock :)

[Matt J]

You're welcome. But if this is related to your other post, and you are trying to solve

   fftshift(fft2(fftshift(x)))) = y

I hope you realize that the solution is just

    x = fftshift(ifft2(fftshift(y))))

In other words, there is no reason to be seeking the matrix representation, F. A linear algebraic solution would also be slower computationally.