FOURIER SERIES PACKAGE SYMBOL

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 .

DetailsDetails

• To use , 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 is defined to be NIntegrate[expr Cos[k t], {t, -, }] and the coefficient is defined to be NIntegrate[expr Sin[k t], {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 is (+ck Cos[2 b k t]+dk Sin[2 b k t]). Here, the coefficient is defined to be NIntegrate[expr Cos[b k t], {t, -, }] and the coefficient 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, can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.

ExamplesExamplesopen allclose all

Basic Examples (1)Basic Examples (1)

Numerical approximation for a trigonometric Fourier series:

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Compare with a plot of the original function:

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TutorialsTutorials

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