Do I need to call fftshift before calling fft or ifft?

Question

In the book "Computational Fourier Optics, A Matlab Tutorial" by David Voelz, it is written that a call to fftshift is needed before a call to fft or ifft, but in the MATLAB documentation of fftshift it's only written that this command

rearranges the outputs of fft, fft2, and fftn by moving the zero-frequency component to the center of the array.

There is no mention in documentation that this command should be called before the call to fft, and I saw some examples that call fft without a call to fftshift beforehand.

My question is: Whether or not fftshift needed to be called before a call to fft or ifft?

If fftshift doesn't need to be called before a call to fft, and only after a call to fft, then when should we use (if at all) the command ifftshift with relation to a calculation of the fft of a data set?

Answer 1

Given the title of the book you are studying, I assume you are working with images. Then the proper way is to call both fftshift and ifftshift before and after you call [i]fft.

Your code should look like

spectrum = fftshift(fft2(ifftshift(myimage))

It is quite the same when applying the inverse Fourier transform

myimage = fftshift(ifft2(ifftshift(spectrum))