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Thread: Fourier transform with | . |

  1. May 30th 2008, 08:13 AM #1
    triptyline
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    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
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  2. May 30th 2008, 09:09 AM #2
    ThePerfectHacker
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    Quote Originally Posted by triptyline View Post
    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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