[Numpy-discussion] Numpy FFT.FFT slow with certain samples

[Charles R Harris]

On Tue, Sep 1, 2015 at 12:06 PM, Oscar Benjamin <oscar.j.benjamin at gmail.com>
wrote:

>
> On Tue, 1 Sep 2015 18:43 Phil Hodge <hodge at stsci.edu> wrote:
>
> On 09/01/2015 11:14 AM, Oscar Benjamin wrote:
> > Just use the next power of 2. Pure powers of 2 are the most efficient
> > for FFT algorithms so it potentially works out better than finding a
> > smaller but similarly composite size to pad to. Finding the next power
> > of 2 is easy to code and never a bad choice.
>
> It would be better to pad to a power of three or five, or some other
> product of small primes, if the pad length would be significantly less
> than padding to a power of two.  The obvious problem with padding is
> that it's different from the real data, so its presence will affect the
> result.  At the least, it would be good to pad with the mean value of
> the original data, or to pad with zero after subtracting the mean from
> the original data.
>
>
>
> I meant performance wise it's not a bad choice. If you're concerned about
> distortion then use the Bluestein algorithm as I showed.
>

I don't see the problem with padding. After all, the spectrum is an
estimate and the effect of the padding, as well as the use of windowing is
well understood. However, I would recommend subtracting the average before
padding, as otherwise the DC frequency is likely to be of large amplitude
and its side lobes will mask the lower frequencies.


> --
> Oscar
>
>
>
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