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Thread: Inverse fourier transform

  1. #1
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    Inverse fourier transform

    Hello everyone!

    I'm trying to IFT this fraction after I couldn't find it in a Fourier couples table.

    $\displaystyle F(j\omega)=\frac{250\pi \delta(\omega)}{30+125\omega}$.
    When I integrated the latter, I got: $\displaystyle \frac{1}{2\pi}\int_{0-}^{0+} \frac{250\pi \delta(\omega)}{30+125\omega}e^{-j\omega t}d\omega$ $\displaystyle \ =\frac{1}{2\pi}\int_{0-}^{0+} \frac{250\pi \delta(\omega)}{30}d\omega$ $\displaystyle =\frac{25}{6} u(t)$??

    Is there ever a $\displaystyle u(t)$ in IFT ??
    Thanks for any help!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by rebghb View Post
    Hello everyone!

    I'm trying to IFT this fraction after I couldn't find it in a Fourier couples table.

    $\displaystyle F(j\omega)=\frac{250\pi \delta(\omega)}{30+125\omega}$.
    When I integrated the latter, I got: $\displaystyle \frac{1}{2\pi}\int_{0-}^{0+} \frac{250\pi \delta(\omega)}{30+125\omega}e^{-j\omega t}d\omega$ $\displaystyle \ =\frac{1}{2\pi}\int_{0-}^{0+} \frac{250\pi \delta(\omega)}{30}d\omega$ $\displaystyle =\frac{25}{6} u(t)$??

    Is there ever a $\displaystyle u(t)$ in IFT ??
    Thanks for any help!
    For any function continuous in a neighbourhood of $\displaystyle 0$ we have:

    $\displaystyle \int_A f(\omega) \delta(\omega)\;d\omega=f(0)$

    For any interval $\displaystyle A$ containing $\displaystyle 0$ as an interior point.

    CB
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  3. #3
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    For any function continuous in a neighbourhood of we have:



    For any interval containing as an interior point.
    Isn't it that $\displaystyle \int_A f(\omega)\delta(\omega) d\omega$ $\displaystyle =\int_A f(0) \delta(\omega) d\omega = f(0)u(t)$
    At least that's what I know from circuit analysis...
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