[Numpy-discussion] numpy.fft, yet again
David Goldsmith
d.l.goldsmith@gmail....
Mon Jul 12 22:26:54 CDT 2010
2010/7/12 Jochen Schröder <cycomanic@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
> >>
> >>
> >>
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set is non-empty, even if that set has measure zero.
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