Digital Signal Processing: Fast Fourier Transform (FFT)

An introduction to the Fourier transform, the magically wonderful mathematical technique that allows us to go from the time domain (i.e. "standard" waveforms") to the frequency domain (i.e. this nifty "frequency spectrum" graphs) and back again.

Links

Although the FFT is widely used, the mathematics involved aren't the most basic DSP that you will find. Understanding how the FFT operates is a terrific step to take in learning how 'hard-core' DSP theory works. The following links are fairly dense for us low-key musicians, but they are pretty fascinating to try to work through the concepts. There are also many many FFT resources on the web (did I mention it was widely used?):

FFT tutorial -- good tutorial
interactive FFT explorer-thingy -- kind of fun to play with; probably more fun if you know what it's doing
FFTW links -- the FFTW people are maniacs. Rather than put a huge number of lins here, just go to this site and click around
Julius O. Smith's FFT page -- also check his "Global Index" for additional FFT (and DFT/DTFT) references

Applications and Examples

We didn't really develop any real 'patches' in this class. Our wonderful guest Michael Klingbeil showed his amaazing SPEAR FFT-based spectral editor software. And we have it! No one else does! Ha ha ha ha ha ha ha!!!!!!!

Soon this will change -- Michael will be making it available to the world when he's ready...

Jason summarized the class:


No patches or anything to give you. We talked about FFTs (including 
windowing, window size, tradeoffs btwn frequency and time resolution, 
etc., etc.) and analyzed a recording of my pathetic attempt to sing in 
Amadeus. I briefly mentioned how fft stuff works in MSP (pfft~) and 
referred them to tutorials 25 and 26 if they want the gory details. 
Talked a little bit about phase vocoding and played a little Larry 
Polansky piece as an example.

Then Michael took over and demo'd Spear, showing us just how cool it is 
and also discussed some ways it differs from "classic" fft analysis. It 
was pretty impressive, as you know, he's going to get the beta version 
on some CMC machines soon.

and the good news is that Michael's software (SPEAR) is in fact installed (beta-version) on several of our studio machines now.