FourierSeries`

NFourierSeries

NFourierSeries[expr,t,n]

gives a numerical approximation to the order n Fourier exponential series expansion of expr, where expr is a periodic function of t with period 2π.

Details and Options

To use NFourierSeries, you first need to load the Fourier Series Package using Needs["FourierSeries`"].
The numerical approximation to the order n Fourier exponential series expansion of expr is by default defined to be F_k^kt, where F_k is given by NIntegrate[expr ^-kt,{t,-π,π}].
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 NFourierSeries is F_k^bkt, where F_k is given by NIntegrate[expr ^-bkt,{t,-,}].
In addition to the option FourierParameters, NFourierSeries can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.

Numerical approximation for an exponential Fourier series:

Compare with a plot of the original periodic function:

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