gives the symbolic Fourier transform of expr.


gives the multidimensional Fourier transform of expr.

Details and Options

  • The Fourier transform of a function is by default defined to be .
  • The multidimensional Fourier transform of a function is by default defined to be .
  • Other definitions are used in some scientific and technical fields.
  • Different choices of definitions can be specified using the option FourierParameters.
  • With the setting FourierParameters->{a,b} the Fourier transform computed by FourierTransform is .
  • Some common choices for {a,b} are {0,1} (default; modern physics), {1,-1} (pure mathematics; systems engineering), {-1,1} (classical physics), and {0,-2Pi} (signal processing).
  • The following options can be given:
  • Assumptions$Assumptionsassumptions to make about parameters
    FourierParameters{0,1}parameters to define the Fourier transform
    GenerateConditionsFalsewhether to generate answers that involve conditions on parameters
  • FourierTransform[expr,t,ω] yields an expression depending on the continuous variable ω that represents the symbolic Fourier transform of expr with respect to the continuous variable t. Fourier[list] takes a finite list of numbers as input, and yields as output a list representing the discrete Fourier transform of the input.
  • In TraditionalForm, FourierTransform is output using . »


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Basic Examples  (2)

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Click for copyable input
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Scope  (6)

Options  (3)

Applications  (4)

Properties & Relations  (3)

Possible Issues  (1)

Neat Examples  (1)

See Also

FourierSinTransform  FourierCosTransform  FourierSeries  FourierCoefficient  Fourier  InverseFourierTransform  FourierSequenceTransform  Convolve  LaplaceTransform  HankelTransform  RadonTransform  Integrate  Piecewise  CharacteristicFunction


Introduced in 1999