2010/7/12 Jochen Schröder <cycoma...@gmail.com> > On 13/07/10 08:04, Eric Firing wrote: > > On 07/12/2010 11:43 AM, David Goldsmith wrote: > >> > From the docstring: > >> > >> "A[0] contains the zero-frequency term (the mean of the signal)" > >> > >> And yet, consistent w/ the definition given in the docstring (and > >> included w/ an earlier email), the code gives, e.g.: > >> > >> >>> import numpy as np > >> >>> x = np.ones((16,)); x > >> array([ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., > >> 1., 1., 1.]) > >> >>> y = np.fft.fft(x); y > >> array([ 16.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, > >> 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, > >> 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j]) > >> > >> i.e., the zero-th term is the sum, not the mean (which, again, is > >> consistent w/ the stated defining formula). > >> > >> So, same ol', same ol': bug in the doc (presumably) or bug in the code? > > > > Bug in the doc. Good catch. "mean" is correct for the ifft, not for > > the fft. > > > > Eric > > > I'd say that a pointer to a discussion about normalization of ffts would > be good here. The issue is that numpy is doing a normalization to len(x) > for the inverse fft. However to make ffts unitary it should actually be > that fft and ifft are normalized by sqrt(len(x)). And some fft > implementations don't do normalizations at all (FFTW). > > Interesting comment: it made me run down the fftpack > tutorial<http://docs.scipy.org/scipy/docs/scipy-docs/tutorial/fftpack.rst/>josef > has alluded to in the past to see if the suggested pointer could point there without having to write a lot of new content. What I found was that although the scipy basic fft functions don't support it (presumably because they're basically just wrappers for the numpy fft functions), scipy's discrete cosine transforms support an "norm=ortho" keyword argument/value pair that enables the function to return the unitary versions that you describe above. There isn't much narrative explanation of the issue yet, but it got me wondering: why don't the fft functions support this? If there isn't a "good" reason, I'll go ahead and submit an enhancement ticket.
DG > Cheers > Jochen > > >> > >> DG > >> > >> > >> > >> _______________________________________________ > >> NumPy-Discussion mailing list > >> NumPy-Discussion@scipy.org > >> http://mail.scipy.org/mailman/listinfo/numpy-discussion > > > > _______________________________________________ > > NumPy-Discussion mailing list > > NumPy-Discussion@scipy.org > > http://mail.scipy.org/mailman/listinfo/numpy-discussion > > _______________________________________________ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion > -- Mathematician: noun, someone who disavows certainty when their uncertainty set is non-empty, even if that set has measure zero. Hope: noun, that delusive spirit which escaped Pandora's jar and, with her lies, prevents mankind from committing a general suicide. (As interpreted by Robert Graves)
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