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.