[Numpy-discussion] Possible typo in numpy.dft.fft docstring
Travis Oliphant
oliphant.travis at ieee.org
Thu Jan 26 06:40:08 CST 2006
Rudolph van der Merwe wrote:
>Part of the fft function's docstring currently reads:
>
>"...
>
>The packing of the result is "standard": If A = fft(a, n), then A[0]
> contains the zero-frequency term, A[1:n/2+1] contains the
> positive-frequency terms, and A[n/2+1:] contains the negative-frequency
> terms, in order of decreasingly negative frequency. So for an 8-point
> transform, the frequencies of the result are [ 0, 1, 2, 3, 4, -3, -2, -1].
>
>..."
>
>Shouldn't the frequency arrangement in the last sentence be
>
>[0, 1, 2, 3, -4, -3, -2, -1]
>
>
>
>and not
>
>[ 0, 1, 2, 3, 4, -3, -2, -1]
>
>
Of course these are completely equivalent because of the periodicity of
the DFT, but the statement A[1:n/2+1] contains the positive-frequency
terms is consistent with what's given. It think the issue is that this
statement is true for both even add odd values of n, while writing it
the way you propose would require different statements for odd and even
terms.
I do typically interpret the middle frequency as "negative" though (as
does fftshift).
-Travis
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