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)

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Numerical approximation for a trigonometric Fourier series:

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Compare with a plot of the original function:

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