FourierSequenceTransform

FourierSequenceTransform[expr,n,ω]
gives the Fourier sequence transform of expr.

FourierSequenceTransform[expr,{n1,n2,},{ω1,ω2,}]
gives the multidimensional Fourier sequence transform.

Details and OptionsDetails and Options

  • FourierSequenceTransform is also known as discrete-time Fourier transform (DTFT).
  • FourierSequenceTransform[expr,n,ω] takes a sequence whose n^(th) term is given by expr, and yields a function of the continuous parameter ω.
  • The Fourier sequence transform of is by default defined to be .
  • The multidimensional transform of is defined to be .
  • The following options can be given:
  • Assumptions$Assumptionsassumptions on parameters
    FourierParameters{1,1}parameters to definite discrete-time Fourier transform
    GenerateConditionsFalsewhether to generate results that involve conditions on parameters
  • Common settings for FourierParameters include:
  • default settings
    {1,-2Pi}period 1
    general setting

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Find the discrete-time Fourier transform of a simple signal:

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Find a bivariate discrete-time Fourier transform:

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Introduced in 2008
(7.0)