# Fourier transform with | . |

• May 30th 2008, 08:13 AM
triptyline
Fourier transform with | . |
Hello,

How do you go about finding the Fourier transform of $e^{-2|t-1|}$. Specifically how do you deal with the | . | part.

Chris
• May 30th 2008, 09:09 AM
ThePerfectHacker
Quote:

Originally Posted by triptyline
Hello,

How do you go about finding the Fourier transform of $f(t) = e^{-2|t-1|}$. Specifically how do you deal with the | . | part.

Chris

You need to calculate,
$F(\omega) = \int_{-\infty}^{\infty} f(t) e^{-2\pi i t\omega} dt$.
Break the integral,
$\int_{-\infty}^{1}e^{2(t-1)} e^{-2\pi i t\omega} dt + \int_1^{\infty} e^{-2(t-1)} e^{-2\pi i t\omega} dt$.
And now compute each one seperately.