Geek: Fourier transforms...

Geek: Fourier transforms...  This is hands-down the best introduction to Fourier transforms I've ever seen – and there's no math in it at all!  And even better, here's a wonderful interactive animation that brings harmonic summation to life in a way I've never seen before.  For some reason I haven't figured out, Fourier transforms are all over slashdot this morning.

I haven't had occasion to use Fourier transforms for years now, but early in my career they were an important part of two engineering projects I undertook.  One was a TTY-on-telephone decoder for the deaf, the other a radio-teletype decoder for ham radio.  These are both “frequency shift keying” (FSK) systems, and both subject to much noise and distortion (though of different kinds in the two cases).  In both the challenge turned out to be primarily one of tricky optimization, trying to compute the Fourier transform well enough to suit the need in near-realtime on the microcomputer hardware of the day.  That hardware typically didn't have multiply or divide (it had to be written in software), and that was the big challenge.  I recall those projects as being chock full of too-clever tricky hacks, things that would be much frowned on these days – but they worked, thanks to the underlying idea of a Fourier transform...