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

dlakelan wrote:
> Raymond Toy wrote:
>> dlakelan wrote:
>>> I am not actually advocating changing what the FFT DOES, only how we
>>> describe what it does, so that people know where the frequencies are.
>>> The current formula in the documentation is true because frequencies
>>> higher than the Nyquist frequency (pi radians per sample) alias
>>> appropriately onto negative frequencies...
> ...
>
>> Ok.  So which formula do you want changed?  The formula for the
>> definition of the FFT?
>
> Yes, and the inverse transform i guess.
>
> For the forward transform, I think we can describe it equivalently as:
>
> y[k] = (1/n) sum (x[j] exp (- 2 %pi %i j k / n )), j, 0, n-1) for k <=
> n/2
> y[k] = (1/n) sum (x[j] exp (- 2 %pi %i j (k-n) / n)), j, 0, n-1) for k
> > n/2
>
> also, I forget, does maxima array indexing start at 0 or at 1? (this
> assumes 0 start)
I think this then makes it harder for someone to know that Maxima's fft
matches that of other definitions.  Why not just put some test pointing
out the negative frequencies are in the second half (in reverse order)?

Ray