In mathematics, a Fourier series decomposes a periodic function or periodic signal into a sum of simple oscillating
functions, namely sines and cosines (or complex exponentials). The study of Fourier series is a branch of Fourier
analysis. Fourier series were introduced by Joseph Fourier (1768–1830) for the purpose of solving the heat equation
in a metal plate. It led to a revolution in mathematics, forcing mathematicians to reexamine the foundations of
mathematics and leading to many modern theories such as Lebesgue integration.  Wikipedia
Here are the Fourier Series for a few of the simplest and most common waveforms.
(See general formula for Fourier Series)

Triangular Wave 

Square Wave 

Halfwave Rectified Sine Wave 

Fullwave Rectified Sine Wave 

