Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.View current documentation (Version 11.2)


gives the symbolic Fourier transform of expr.

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