A question on fftshift

[Steve M. Robbins]

Hi,

I hope someone can tell me if the bug lies in the fftshift doc or
my comprehension.

My understanding of the discrete Fourier transform, confirmed by
Numerical Recipes

  http://www.ulib.org/webRoot/Books/Numerical_Recipes/bookcpdf/c12-1.pdf

is that the frequency interval for the FFT output is [-fc,fc] where fc
is the critical (Nyquist) frequency.

For samples spaced Dt apart, fc = 1/(2*Dt), so I expect the output
range to be [-1/(2*Dt),1/(2*Dt)].  Or, rather, the standard "wrapped"
sequence of this.  Thus, I would expect that after "fftshift", the
frequency values for the sample points should be

  linspace( -1/(2*Dt), 1/(2*Dt) - 1/(N*Dt), N )

for an input of N samples.

The documentation for fftshift says otherwise, however.


 - Function File:  fftshift (V)
     Perform a shift of the vector V, for use with the `fft' and `ifft'
     functions, in order the move the frequency 0 to the center of the
     vector or matrix.

     If V is a vector of E elements corresponding to E time samples
     spaced of Dt each, then `fftshift (fft (V))' corresponds to
     frequencies

          f = linspace (-E/(4*Dt), (E/2-1)/(2*Dt), E)


Who is correct?

Thanks,
-Steve



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