On 2/5/07, Hanno Klemm <[EMAIL PROTECTED]> wrote: [numpy.fft[
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].
[scipy.fft] f = [0,1,...,n/2-1,-n/2,...,-1]/(d*n) if n is even
f = [0,1,...,(n-1)/2,-(n-1)/2,...,-1]/(d*n) if n is odd >>> So one claims, that the packing goes from [0,1,...,n/2,-n/2+1,..,-1] (fft) and the other one claims the frequencies go from [0,1,...,n/2-1,-n/2,...-1] Is this inconsistent or am I missing something here?
Both, I think. In the even case, the frequency at n/2 is shared by both the positive frequencies, so for that case things are consistent if not terribly clear. For the odd case, this is not true, and the scipy docs look correct in this case, while the numpy docs appear to assign an extra frequency to the positive branch. Of course that's not the one you were complaining about ;-). To be super pedantic, the discrete Fourier transform is periodic, so all of the frequencies can be regarded as positive or negative. That's not generally useful, since the assumptions that go into the DFT that make it periodic don't usually apply to the signal that you are sampling. Then again the results of DFTs are typicallly either small or silly in the vicinity of N//2. //=][=\\ [EMAIL PROTECTED]
_______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion