NFourierTrigSeries

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

Details and Options

To use NFourierTrigSeries, 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 c₀+c_kCos[k t]+d_k Sin[k t].
The coefficient c_k is defined to be NIntegrate[expr Cos[k t],{t,-π,π}] and the coefficient d_k is defined to be NIntegrate[expr Sin[k t],{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 NFourierTrigSeries is (+c_k Cos[2π b k t]+d_k Sin[2π b k t]). Here, the coefficient c_k is defined to be NIntegrate[expr Cos[b k t],{t,-,}] and the coefficient d_k is defined to be NIntegrate[expr Sin[b k t],{t,-,}].
The parameter b in the setting FourierParameters->{a,b} must be numeric.
In addition to the option FourierParameters, NFourierTrigSeries can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.