Fourier transform with | . |

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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.

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