fftshift/ifftshift

Question

Please, see the the description of both fftshift and ifftshift. I would like to understand how to call the above two functions in relationship with fft and fftn in Matlab.

Let say that my signal has a certain frequency content; now, the frequency array can generally be stored as:

f = (-N/2:N/2-1)*df;

f = (1:N)*(df/2);

f = [(0:N/2-1) (-N/2:-1)];

What is the best way to call fft, coupled with fftshift and ifftshift, for the 3 study cases early mentioned?

What is the effect on the standard deviation of the signal of calling the sequence of commands or the wrong one?

This question encouraged me to ask an extensive question about the topic here: http://stackoverflow.com/questions/19901519/shifting-indexes-similar-to-fftshift-in-matlab-for-own-range — Léo Léopold Hertz 준영, Nov 11 '13 at 08:06

score 7 · Accepted Answer · answered Feb 26 '13 at 22:05

7

The result of fft is (in your notation) indices (0:N-1). fftshift simply converts that to [(N/2:N-1) (0:(N/2-1))].^* ifftshift simply restores the original indexing.

As this is simply reordering samples, it does nothing to the standard deviation.

_{* Note that due to periodicity, sample k is equivalent to sample k+N, or k-N, etc.}

answered Feb 26 '13 at 22:05

Oliver Charlesworth

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and the input of the `fft` is expected to be swapped or un-swapped? – fpe Feb 26 '13 at 22:08
@fpe: I don't understand what you're asking. The output of `fft` is what it is, `(0:N-1)`. – Oliver Charlesworth Feb 26 '13 at 22:09
I would like to understand if fft in Matlab expects to have input in the standard notation `(-N/2:N/2-1)*df` or not – fpe Feb 26 '13 at 22:11
@fpe: The **input** to `fft` is **time**-domain data. The **output** is **frequency**-domain data, in frequency order `(0:N-1)`. – Oliver Charlesworth Feb 26 '13 at 22:12
2

http://www.mathworks.com/matlabcentral/newsreader/view_thread/285244 is probably the answer I was looking for – fpe Feb 26 '13 at 22:20

Konstantin Burlachenko · Answer 2 · 2016-04-28T21:55:15.760

Matlab documentation is just killing about it. But experiments show that

ifftshift([1 2 3 4 5])

ans =

 3     4     5     1     2

fftshift([1 2 3 4 5])

ans =

 4     5     1     2     3

It is just swapping around the magic DFT position [N/2]. FFT implemented in matlab use usual indexing (0:N-1). As I understand this is extra functions to prepare your input to DFT if your setup is dicrete function not in (0:N-1)...

fftshift/ifftshift

2 Answers2

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