Examples Using Complex Fourier Series

This is an evaluated Mathematica notebook. Since the notebook is intended to be interactive, it may be helpful to also view the unevaluated version


Copyright 1996
Gary S. Stoudt
Mathematics Department
Indiana University of PA
Indiana, PA 15705
GSSTOUDT@grove.iup.edu

Fourier series can be written as
a0+Sum{n=1 to Infinity} [an cos(nwx) + bn sin(nwx)], where w=2 Pi/p, p the fundamental period (use interval -p/2 to p/2 instead of -L to L). The an and bn coefficients are given in the usual way.

A series can also be written as
Sum{n=-Infinity to Infinity} cn Exp(I nwx), where w=2 Pi/p and the coefficients are given by

cn = 1/p Integral{-p/2 to p/2} f(t) Exp(I nwt) dt

This notebook simply shows for two examples that these are equivalent. A proof can be found in most textbooks.

Absolute Value of x from -Pi to Pi.

Ramp-Like Function

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