FourierTransform

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

Examples

Fourier transform of a Gaussian:

FourierTransform[Exp[-t^2], t, ω]
(* E^(-ω^2/4)/Sqrt[2] *)

Rectangular function:

FourierTransform[UnitBox[t], t, ω]
(* Sinc[ω/2]/Sqrt[2 Pi] *)

Please visit the official Wolfram Language Reference for more details.