NFourierSeries
FourierSeries`
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
Fkkt, where Fk 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 
Fkbkt, where Fk 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.
Examples
Basic Examples (1)
Needs["FourierSeries`"]Numerical approximation for an exponential Fourier series:
NFourierSeries[Sin[Cos[t]] + Abs[t] / 5, t, 4, FourierParameters -> {1, -2π}] //ChopPlot[%, {t, -2, 2}]Compare with a plot of the original periodic function:
Plot[Sin[Cos[(t - Round[t])]] + Abs[t - Round[t]] / 5, {t, -2, 2}]