FourierCoefficient

FourierCoefficient[expr,t,n]
gives the n^(th) coefficient in the Fourier series expansion of expr.

FourierCoefficient[expr,{t1,t2,},{n1,n2,}]
gives a multidimensional Fourier coefficient.

Details and OptionsDetails and Options

  • The ^(th) coefficient in the Fourier series expansion of is by default given by .
  • The -dimensional Fourier coefficient is given by .
  • In the form FourierCoefficient[expr,t,n], n can be symbolic or an integer.
  • The following options can be given:
  • Assumptions$Assumptionsassumptions on parameters
    FourierParameters{1,1}parameters to define Fourier series
    GenerateConditionsFalsewhether to generate results that involve conditions on parameters
  • The function expr is assumed to be periodic in t with period , except when otherwise specified by FourierParameters.
  • Common settings for FourierParameters include:
  • {1,1}f(t) e-i n tdtdefault settings
    {1,-2Pi}f(t) ei 2π n tdtperiod 1
    {a,b}general setting

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Find the 5^(th) Fourier coefficient:

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Find the coefficient of the general term in a Fourier series:

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Plot the sequence:

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Find the Fourier coefficient:

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Find the coefficient of the general term:

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Plot the absolute value of coefficients:

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Introduced in 2008
(7.0)