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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  