The Fourier transform of a Gauss function f(x)=e−Ax2f(x)=e^{-Ax^2}f(x)=e−Ax2 is given as follows.
F[f](ξ)=F[e−Ax2](ξ)=πAe−ξ24A \mathcal{F}[f] (\xi) = \mathcal{F} \left[ e^{-Ax^2} \right] (\xi)=\sqrt{\frac{\pi}{A}}e^{-\frac{\xi ^2}{4A}} F[f](ξ)=F[e−Ax2](ξ)=Aπe−4Aξ2
