Fourier Series Animation using Circles

“Any periodic signal can be decomposed into a set of simple oscillating functions (also known as harmonics) via the application of Fourier series expansion. Here, we demonstrate a few harmonics using circles and how they add up to obtain the resulting function. Each circle spins at a multiple of a certain fundamental frequency. First, we show each harmonic individually and later show what they add up to and how the circles can be used for their visualization.”

Fourier series are an incredibly useful tool for digitizing data, removing noise from signals, etc. The mathematics behind Fourier transforms requires a bit of calculus, but the concept can be explained visually in a rather elegant manner.

Fourier Series Animation using Circles