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.

Source: Fourier Series - See more at Fourier Series on mathworld.wolfram.