# An inverse fourier transform

1. Jan 9, 2012

### atrus_ovis

1. The problem statement, all variables and given/known data
(part of a problem)
Find the inverse fourier of F(w) = (3jw+9)/((jw)^2+6jw+8)
where w is the angular frequency, w=2pi * f = 2*pi/T

2. Relevant equations
The fourier transfrom and its properties i guess.
Also the exponential FT common pair exp(-at)u(t) <-> 1/(jw+a)
where exp is the exponential function and u(t) the unit step function

3. The attempt at a solution
I factored out the denominator in a hope that the 3jw+9 would cancel out with a possible root of jw=-3 , but the roots are -2 and -4.
I've been trying to seperate F into a product of easy transformable parts, to take advantage of the convolution property : x(t) [convolve] f(t) = X(w)F(w) , but i cant get rid of the nominator to apply the exponential fourier pair.
Any hints?

2. Jan 9, 2012

### atrus_ovis

If the nominator was a constant, i could break it into simple fractions.
Can you do it if it's not a constant?

3. Jan 9, 2012

### atrus_ovis

^
Ah,nevermind, you can.
case closed.