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Math Help - Fourier Transform Problem

  1. #1
    Junior Member
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    Fourier Transform Problem

    I'm having a bit of an issue working out the following problem

    p(t) =

    1, for |t|<= 0.5
    0, for |t| > 0.5

    Can someone give me some help with this please?
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  2. #2
    Super Member Deadstar's Avatar
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    Quote Originally Posted by jezzyjez View Post
    I'm having a bit of an issue working out the following problem

    p(t) =

    1, for |t|<= 0.5
    0, for |t| > 0.5

    Can someone give me some help with this please?
    \hat{f}(\xi) = \int_{-\infty}^{\infty} p(t) e^{-2\pi i \xi t} dt

    = \int_{-0.5}^{0.5} e^{-2\pi i \xi t} dt.

    can ya finish..?
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  3. #3
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    Quote Originally Posted by Deadstar View Post
    \hat{f}(\xi) = \int_{-\infty}^{\infty} p(t) e^{-2\pi i \xi t} dt

    = \int_{-0.5}^{0.5} e^{-2\pi i \xi t} dt.

    can ya finish..?
    Does it work through to \frac {\sin \pi \omega}{2 \pi \omega}?
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  4. #4
    Super Member Deadstar's Avatar
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    Quote Originally Posted by jezzyjez View Post
    Does it work through to \frac {\sin \pi \omega}{2 \pi \omega}?
    I got \frac{\sin(\pi \xi)}{\pi \xi} (by the way latex for \xi is \xi.)
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