Hallo!

> "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?

No - the term "fast" fourier transform comes from the special algorithm 
how the DFT (discrete fourier transform) is calculated (see e.g. 
http://en.wikipedia.org/wiki/Fft)

LG
Georg

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