InverseFourierTransform

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

Examples

Inverse transform:

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

Round-trip verification:

InverseFourierTransform[FourierTransform[f[t], t, ω], ω, t]
(* f[t] *)

Please visit the official Wolfram Language Reference for more details.