I suppose this should belong in a blog or a post but it's more of a question because I don't present anything, but I merely pose an interesting question and wondered if anyone was up to the challenge. This is also related to Deconstructiong a wave http://www.mapleprimes.com/questions/124373-Deconstruct-A-Waveform-Into-Its-Fundamental
Recently I read an interesting article in the June 2011 issue of Discover magazine about a new way of audio compression. Basically the compression involves describing the sound waves as geometric shapes "object based compression" they called it. This approach says that they can reduce the file size by about 50% as compared with mp3's. The technique involves plotting the music over time in frequency and amlitude resulting in a 3d mountainscape. Visualizing the recording like this allows you to describe the music in terms of geometric shapes instead of many frequencies ... akin to describing a circle by it's center point and radius rather than with many little segment points of the circle.
It is an interesting concept. And the really fun part ... who can recreate the technique in Maple?
I thought it is similar in comparing djvu compressed files which uses unconventional compression methods in that it stores the individual positions of each letter rather than compressing the complete content by other means.