for your info: ch. 11 mbe: fast fourier transforms

On 5/5/09, dlakelan <dlakelan at street-artists.org> wrote:

> Robert Dodier wrote:
>> Well, I dunno. The computed results match the stated definition --
>> I've verified that directly. We could pick a different definition, I
>> guess, if it could make the results more useful or comprehensible.
>
> Yes perhaps this is the thing to do. I think the point is to help the
> users of the fft routine when doing something relatively standard, such
> as fft transforming a real function, and trying to manipulate the
> individual frequencies.

Having thought it over, I'm opposed to changing the definition of
the FFT for Maxima.

I'm pretty sure the FFT definition should be general, and not
embody some particular assumption about what people are trying
to do. Maybe in some cases it's safe to make assumptions, but it
certainly isn't for FFT.

> perhaps an alternative would be to provide a "rfft" and "irfft" that
> handles purely real data in a "nice" way for the user?

I dunno. Hmm. Maybe there could be a function to compute the
cos and sin coefficients from the transform output (as a post-
processing step instead of another transform function). I don't
want to get into the business of inventing different varieties of
FFT.

best

Robert Dodier