# Thread: Fourier Transform - Scaling Property

1. ## Fourier Transform - Scaling Property

$\displaystyle Find the Fourier transform of \frac{1}{p}e^{\frac{-\pi x^2}{p^2}}$ for any $p > 0$. I know that the Fourier transform of $e^{-\pi x^2}$ is $e^{-\pi u^2}$. I was told to use the scaling property also. After attempting the problem I came up with $\frac{1}{p}e^{\frac{-\pi u^2}{p}$. I am not sure if this is right though. \$

2. ## Re: Fourier Transform - Scaling Property

Hey rogerwilliamsi27.

The scaling property of a fourier transform is given as:

F(h(ax)) = 1/|a| * F(e/a) where F is the fourier transform in frequency space e.

Fourier transform - Wikipedia, the free encyclopedia

You can prove it by replacing x with ax and simplifying.