Google for FFTW..."Fastest Fourier Transform [in the] West" lol
It was developed by Frigo & Johnson at MIT...I've met the latter.
Now that's a fast fourier transform 😉
Edit: but really, unless you're going to delve deep into how these advanced algorithms work, the basic cooley-tukey (sp) algorithm is a good baseline to read & understand. Anything more than that is really overkill...because well, you're not going to write something faster than say FFTW anytime soon 😛