Different results interchanging fftshift and unwrap

I have found that I get very different phase spectra when using FFT without fftshift or unwrap, FFT with fftshift then unwrap, and FFT with unwrap then fftshift. Any ideas as to why and which is correct?

Answer 1

[Wayne King]

Hi Bruce, unwrap() works on the vector in order from the 1st element to the last. It stands to reason if you use fftshift first and then call unwrap, you have a different order of phase shifts. unwrap() just looks for jumps of more than pi radians and goes to work, so

unwrap(angle(fft(x)))

and

unwrap(angle(fftshift(fft(x))))

are very likely not going to experience >pi radian shifts in phase at the same elements.

Suppose you have the following 8-point DFT.

   xdft = [-3.1344 + 0.0000i
   2.3474 - 0.1296i
  -0.1774 - 1.5397i
  -1.9544 - 0.5292i
  -2.4890 + 0.0000i
  -1.9544 + 0.5292i
  -0.1774 + 1.5397i
   2.3474 + 0.1296i]

Then

ang = angle(xdft)

yields:

ang = 

     3.1416
     -0.0552
     -1.6855
     -2.8772
      3.1416
      2.8772
      1.6855
      0.0552

You see that from element 1 to 2, there is more than a pi radian shift, so that

unwrap(ang)

gives you -0.0552+(2*pi) for the 2nd element.

but:

angle(fftshift(xdft))

does not show more than a pi radian jump from element 1 to 2 (because the elements have been reordered), so

 unwrap(angle(fftshift(xdft)))

does not affect the 2nd element.