The smooth motion of rotating circles can be used to build up any repeating curve even one as angular as a digital square wave. Each circle spins at a multiple of a fundamental frequency, and a method called Fourier analysis shows how to pick the radiuses of the circles to make the picture work. Decomposing signals like this lies at the heart of a lot of signal processing. [more] [code]
Fourier Transform was a topic that, I assumed, marked the end of being able to visualize the concepts in my education. Until now!