FourierSeries`
FourierSeries`

# NFourierTrigSeries

NFourierTrigSeries[expr,t,k]

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+ ckCos[k t]+dk Sin[k t].
• The coefficient ck is defined to be NIntegrate[expr Cos[k t],{t,-π,π}] and the coefficient dk 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 ( + ck Cos[2π b k t]+dk Sin[2π b k t]). Here, the coefficient ck is defined to be NIntegrate[expr Cos[b k t],{t,- , }] and the coefficient dk 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.

# Examples

## Basic Examples(1)

Numerical approximation for a trigonometric Fourier series:

Compare with a plot of the original function: