# Inverse fourier Transform of 1/(1+.5jw)

• Nov 13th 2011, 05:03 AM
moonnightingale
Inverse fourier Transform of 1/(1+.5jw)
Hi the inverse fourier transform of

1/(alpha+jw) is u(t)exp(-alpha x t)

but what if there is some term with jw like 1/(1+.5jw)
how it will be catered
I could not see such example in any fourier transform table

Plz guide me
• Nov 21st 2011, 10:30 AM
TheEmptySet
Re: Inverse fourier Transform of 1/(1+.5jw)
Quote:

Originally Posted by moonnightingale
Hi the inverse fourier transform of

1/(alpha+jw) is u(t)exp(-alpha x t)

but what if there is some term with jw like 1/(1+.5jw)
how it will be catered
I could not see such example in any fourier transform table

Plz guide me

Just build the fraction by multiplying by $\displaystyle \frac{2}{2}$

$\displaystyle \frac{1}{1+.5jw}=\frac{2}{2}\cdot \frac{1}{1+.5jw}=\frac{2}{2+jw}$

Just remember that the inversve transform is linear so

$\displaystyle F^{-1}\left( \frac{2}{2+jw} \right) =2F^{-1}\left( \frac{1}{2+jw} \right)$