Fourier Transform of Gaussian Functions
Formulas
The Fourier transform of a Gauss function $f(x)=e^{-Ax^2}$ is given as follows.
$$ \mathcal{F}[f] (\xi) = \mathcal{F} \left[ e^{-Ax^2} \right] (\xi)=\sqrt{\frac{\pi}{A}}e^{-\frac{\xi ^2}{4A}} $$
The Fourier transform of a Gauss function $f(x)=e^{-Ax^2}$ is given as follows.
$$ \mathcal{F}[f] (\xi) = \mathcal{F} \left[ e^{-Ax^2} \right] (\xi)=\sqrt{\frac{\pi}{A}}e^{-\frac{\xi ^2}{4A}} $$