[PD] fft beginner question
thomas at dergrossebruder.org
Wed Nov 21 11:57:46 CET 2007
hard off wrote:
> ah cheers frank, thanks for clearing a lot of that up. you do really
> good explainations.
> "The main reason we use complex numbers in electronic music is
> because they magically automate trigonometric calculations. We
> frequently have to add angles together in order to talk about the
> changing phase of an audio signal as time progresses (or as it is
> shifted in time, as in this chapter). It turns out that, if you
> multiply two complex numbers, the argument of the product is the sum
> of the arguments of the two factors."
> so, is that where 'fast' fourier transform comes from then?
Not really, as multiplication is one mathematical operation. 'Fast' in
FFT means reducing the number of mathematical operation from O(N²) to
O(N log N), where N is the number of analyzed frequencies, e.g. for 64
frequencies from (a constant factor times) 64²=4096 to (another constant
factor times) 64 * log(64)~116 operations.
"Prisons are needed only to provide the illusion that courts and police
are effective. They're a kind of job insurance."
(Leto II. in: Frank Herbert, God Emperor of Dune)
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