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Fourier series

Fourier series work by summing specific sine waves to approximate a periodic function such as a square wave. The Fourier series for the square wave is:

\[y=\sum_{n=1}^{N}{\frac{\sin((2n-1)x)}{2n-1}}\]

\(N=1,2,3\) are shown with the red, blue, and purple curves, \(N=100\) is the black curve, and the square wave function is the green line which the fourier series equals when \(N=\infty\).