# inverse Fourier transform

• May 26th 2011, 05:42 PM
morganfor
inverse Fourier transform
How does one show that the inverse Fourier transform of e^-a|y|, a>0 is

(a/pi)*1/(x^2+a^2)

thanks!
• May 26th 2011, 07:49 PM
TKHunny
Have you considered the definition of the Transform?
• May 27th 2011, 07:47 AM
morganfor
Yes, but I'm confused about how to integrate e^-a|y|*e^-iyx to get that answer
• May 27th 2011, 08:23 AM
Ackbeet
I would probably use the equation

$|y|=\begin{cases}y,\quad &y\ge 0\\ -y,\quad &y<0\end{cases},$

and then split up your integral into two pieces depending on which of the two cases is applicable.