How does one show that the inverse Fourier transform of e^-a|y|, a>0 is

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

thanks!

Printable View

- May 26th 2011, 06:42 PMmorganforinverse 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, 08:49 PMTKHunny
Have you considered the definition of the Transform?

- May 27th 2011, 08:47 AMmorganfor
Yes, but I'm confused about how to integrate e^-a|y|*e^-iyx to get that answer

- May 27th 2011, 09:23 AMAckbeet
I would probably use the equation

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