Re: [Maxima-discuss] Fourier Transform , almost symbolic

[Raymond T. <toy...@gm...>]

>>>>> "Robert" == Robert Dodier <rob...@gm...> writes:

    Robert> On 2014-12-02, Edward Montague <qui...@gm...> wrote:
    >> Is this a valid approach , from first principles
    >> it appears to be valid , of course the digital
    >> computation might have a few surprises.

    Robert> Not sure what you are proposing -- there is a function naive_ft in
    Robert> share/numeric/rtest_fft.mac which implements the FFT via direct
    Robert> computation of the summation. Of course that's less efficient than
    Robert> the FFT, but it allows for exact results, and symbolic results.
    Robert> Maybe that's useful in some contexts.

    Robert> It seems like it should be possible to implement the FFT in Maxima
    Robert> using general multiplication and addition (not assuming float
    Robert> arguments) -- perhaps that's the best of both worlds.

I don't really see the utility of an actual FFT supporting symbolic
(or integer) args.  Unless you're saying to compute a symbolic DFT,
which seems useful only if the sum can be simplified into some non-sum
form.

However, I've done something like this ago) for discrete cosine
transforms just using maxima's sum and nusum (no simplify_sum way back
then).  It worked for what I needed, but only because the sums could
be simplified away to other expressions.

Ray