Image 1: Visualisation of an approximation of a square wave by taking the first 1, 2, 3 and 4 terms of its Fourier series. θ is 2πt.
Image 2: Visualisation of an approximation of a sawtooth wave of the same amplitude and frequency for comparison.
In mathematics, a Fourier series is a way to represent a wave-like function as a combination of simple sine waves. More formally, it decomposes any periodic function or periodic signal into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines (or complex exponentials).
Image 4 - 5: A simple Fourier series.
Plot of a periodic identity function, a sawtooth wave & Animated plot of the first five successive partial Fourier series.