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FourierSeries`

FourierSeries`

FourierSeries

As of Version 7.0, FourierSeries is part of the built-in Wolfram System kernel.

FourierSeries[expr,t,n]

gives the order n Fourier exponential series expansion of expr, where expr is a periodic function of t with period 1.

Details and Options

To use FourierSeries, you first need to load the Fourier Series Package using Needs["FourierSeries`"].
The order n Fourier exponential series expansion of expr is by default defined to be F_k^2πkt, where F_k is given by Integrate[expr ^2πkt,{t,-,}].
Different choices for the period of expr can be specified using the option FourierParameters.
With the setting FourierParameters->{a,b}, expr is assumed to have a period of , and the order n Fourier exponential series expansion computed by FourierSeries is F_k^2πkt, where F_k is given by bIntegrate[expr ^2πbkt,{t,-,}].
In addition to the option FourierParameters, FourierSeries can also accept the options available to Integrate. These options are passed directly to Integrate.

Examples

Basic Examples (1)

Compute the exponential Fourier series for a periodic function with period 1:

Compare with a plot of the original function:

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