# Inverse fourier transform

#### 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!

#### CaptainBlack

MHF Hall of Fame
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

#### rebghb

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...