FourierTransform

FourierTransform[expr,t,ω]
gives the symbolic Fourier transform of expr.

FourierTransform[expr,{t1,t2,},{ω1,ω2,}]
gives the multidimensional Fourier transform of expr.

Details and OptionsDetails and Options

  • The 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 are (default; modern physics), (pure mathematics; systems engineering), (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 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 . »
Introduced in 1999
(4.0)