1. ## 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!

2. Originally Posted by rebghb
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

3. 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...