# FFT on circularly symmetric function

I have an circularly symmetric image in Fourier space:

where the 0-frequency is in the center. Now, I want to take the FFT of this image. Having numpy's FFT conventions in mind (i.e. 0 frequency at (0,0)), I first apply the the inverse-fftshift, and then apply the inverse-fourier transform. As follows:

image = np.fft.ifft2(np.fft.ifftshift(FT_image))


This results in the following real space image:

But I can't really wrap my head around this result. It looks as if another fftshift would be in order, but in real space this shouldn't be necessary. I would expect a radially symmetric transform, centered in the center of the image.

Is this expectation wrong, or is my computation wrong? And either way: can you explain why?

• The second image looks to me like it hasn't had the IFFT applied. It looks just like a shifted version of the first one. – Jason R Nov 2 '15 at 15:33
• Pretty much, although the circular pattern extends out further in the second image (so it has definitly been transformed). – user1991 Nov 2 '15 at 16:35