for your info: ch. 11 mbe: fast fourier transforms

On 5/3/09, dlakelan <dlakelan at street-artists.org> wrote:

> Hi Robert, did you see my suggestions for the documentation of the fft
> routine about a month ago? The documentation made it seems like the
> frequencies involved were 0 to 2%pi radians per sample, but in fact they
> are 0 to %pi followed by -%pi up to -%pi/n [...]

Yes, I saw that. After trying some examples, I guess I don't understand
what you're getting at. The results seem to match the definition of the
transform stated in the documentation:

  y[k]: (1/n) sum (x[j] exp (-2 %i %pi j k / n), j, 0, n-1)

i.e. the k'th element is associated with frequency k*2*%pi/n.
I wrote a function to apply the above formula and it matches
the result of fft. So it seems the code and documentaton are
in agreement. Can you explain again in what sense they aren't?
Does it have something to do with coefficients for complex
exponentials vs sin/cos coefficients?

best

Robert Dodier