Examples Using Complex Fourier Series

This is an unevaluated Mathematica notebook. If you do not have a copy of Mathematica handy, you may want to also view the evaluated 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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