Email From Wellons

I just got back in touch with a life-long friend, and asked him a technical question about sound and mathematics, now, I know a little about FFT (Fast Fourier Transform) Just from my musical self-training... BUT now he's pointed me to a little more knowledge, which I will share with you, dear reader.

Any periodic function, like those saw-tooth, triangle, square waves,
can be produced by summing up a series of sine waves. I.e. the Fourier
series,

http://mathworld.wolfram.com/FourierSeries.html

http://en.wikipedia.org/wiki/Fourier_series

And, if you spend a couple years studying a series of numbers between
-1 and 1 (or any arbitrary bounds, really), you have almost earned
yourself an electrical engineering degree. What I am saying is, this
is a field called signal processing, and is a gigantic field of study
which some people have devoted their entire lives to, so you should
have no shortage of interesting things to see playing with this. ;-)

Your basic .wav file is the same thing: just an uncompressed series of
samples. If you write a program to dump these samples to a file in
binary form, then add the proper header, you have a .wav file. Also
see Fourier transforms and frequency domain filters.

Just as audio is a 1-dimensional signal, images are 2-dimensional
signals. Videos are 3-dimensional signals. The same theory applies to
them as well.

You can check out his blog @ http://nullprogram.com/