Fourier analysis allows your cell phone or MP3 player to transmit your voice and play music without needing huge reel-to-reel tape recorders to store all the sounds and without using enormous amounts of bandwidth. It’s now done electronically, by clever mathematical algorithms that are encoded on the tiny microchips inside your computer or cellphone or iPod or whatever.
The general idea is you take a complex wave-front and you turn it into an infinite series of sine or cosine waves. Believe it or not, it actually makes the data much simpler!
A very simple example. This weird shape
is merely the sum of two cosine waves:
And all of the music you hear (eg a clarinet, which might look like this on an oscilloscope)
can be deconstructed into a whole lot of sines or cosines
About 40 years ago, I did some Fourier transforms by hand in a calculus class. It was time-consuming, but very, very cool.
A full century ago, Albert Michelson had to do a whole bunch of Fourier transforms for some astronomy task. It was too time-consuming to do by hand, so he built a machine with gears, levers and so on to do it for him.
It’s a super-cool analog (as opposed to digital) computer — and there is a fellow who shows you exactly how it works!
His presentation is in four parts. Start with this one, the introduction.