**FOURIER SERIES OF A SQUARE-WAVE**

**(GIBBS Phenomenon)**

The Fourier series of a square-wave can be expressed as [Kamen-Heck, pp.148-154]:

f_{square}(t) = (1/2) + (2/pi)*cos(pi*t) + (2/(3*pi))*cos(3*pi*t-pi)
+ ...

The following applet shows how this approximation works. Use the slider to include more and more terms and see what happens. Interestingly, the approximation does not converge to the true value of the square-wave at the points of discontinuities! This is called the Gibbs phenomenon.

This file was last edited on: 04-Jun-01