Fourier Transform - Scaling Property

• Apr 9th 2013, 02:45 PM
rogerwilliams257
Fourier Transform - Scaling Property
$Find the Fourier transform of \frac{1}{p}e^{\frac{-\pi x^2}{p^2}} for any p > 0. I know that the Fourier transform of e^{-\pi x^2} is e^{-\pi u^2}. I was told to use the scaling property also. After attempting the problem I came up with \frac{1}{p}e^{\frac{-\pi u^2}{p}. I am not sure if this is right though.$
• Apr 9th 2013, 06:24 PM
chiro
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.