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FourierTransform[expr, t, ]
gives the symbolic Fourier transform of expr.
FourierTransform[expr, {t1, t2, ...}, {1, 2, ...}]
gives the multidimensional Fourier transform of expr.
  • The Fourier transform of a function f(t) 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.
  • Some common choices for {a, b} are {0, 1} (default; modern physics), {1, -1} (pure mathematics; systems engineering), {-1, 1} (classical physics), {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, ] 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.
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