# Gausian distributions in the Frequency domain

I have read in many texts that the Fourier Transform of a Gaussian is yet another Gaussian, however how does the mean and standard deviation change?

Also if we convolve a Gaussian with itself then we get a wider Gaussian, this is equivalent to the product with the Fourier Transform of the Gaussian with itself. Will this still be a wider Gaussian?

Thanks

-
This is in every elementary textbook (AND you can do the computation yourself) so I would not call this a research level question. Voting to close. –  Igor Rivin Mar 29 '12 at 15:23

The formula for transforming a 0 mean Gaussian says $F_x$e^{-ax^2}$(k)=\sqrt{\frac{\pi}{a}}e^{-\pi^2k^2/a}$ so the standard deviation certainly changes. Indeed the inverse proportionality is an example of the Heisenberg phenomenon.