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Re: [Octal-dev] Fourier Transforms and samples


From: Steve Mosher
Subject: Re: [Octal-dev] Fourier Transforms and samples
Date: Mon, 22 May 2000 01:05:26 -0300

On Fri, 19 May 2000, address@hidden wrote:
>   Do you mean by performance: the processing time required (most like-
>   ly), or the resulting audio quality?

        Performance-wise.

>   But before going onto these questions,  it appears that you have im-
>   plemented or found an STFT implementation. If this is code/software,
>   where can it be found?

        I've found some nice info on STFT (www.dspdimension.com), there's
some example code there as well.

>   In terms  of speed,  if only the generating  phase  (reverse Fourier
>   Transform)  from a predetermined  Fourier description could be used,
>   the forward  transform phase could be avoided.   The STFT method de-
>   scribed (thanks to your previous web reference) on

        Hai, this is what I'm talking about...

<kersnip>

>   As just suggested,  the forward  transform  process should provide a
>   precise Fourier description  to minimize overall processing time but
>   will obtain a trade-off between processing time and precision of re-
>   sult--as seen in the increase of FFTs per sample--to minimize Fouri-
>   er description distortion (with respect to the original sound).

        Hmm... sounds right.

>   But finally,  the STFT process will obtain a floor amount of distor-
>   tion  (some necessary portion of distortion) because of the inherent
>   block nature of the FFT.  This effect will be most apparent at high,
>   transient  frequencies  (discussed  in the parameter  trade-offs  in
>   (1)).

        Yeah, I'm aware of this. Not too worried, unless it becomes
unusable at the point where it can be done in real time.

>   As mentioned  by Davíð B. Franzson,  obtaining a precise Fourier de-
>   scription in something close to real-time will require a significant
>   computational ability. Fourier processing is highly parallel and may
>   be pipelined,  such that I expect a Beowulf Cluster  would  approach
>   the real-time  result.   A one  megahertz  Beowulf  node using AMD's
>   Athlon is closing  in on $1,000.   This kind  of Fourier  processing
>   equipment might be suitable for recording studios where the time re-
>   quired to record and then playback would minimize the processing de-
>   lay issue. The computationally intensive forward transform should be
>   able provide a simplified,  precise Fourier  description  within the
>   record  to playback time delay  and such that the reverse  transform
>   could be processed in real time.  Or is someone already doing this?

        There ought to be sound cards that do this... to boot, clusters
are impractical for home use, not so bad for studio use (good idea,
actually), and horrible for set use. It would be -sweet- to see a cluster
devoted to processing FFTs -- it could be optimized to do simply that, and
a higher load could be placed on it. It would be more useful to have it
perform all your DSP... then again, wouldn't it be more efficient (and
cheaper) to rip apart a PSX2 and use the sound syntesizer? I still want to
see Octal ported to it =). I think it would be the best platform thus far
for such a program...

        Thanks for your reply, highly detailed.

-- 
        Heuristics are bug ridden by definition. If they didn't have bugs, then
they'd be algorithms.


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