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.
cu Thomas
"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) http://thomas.dergrossebruder.org/