# Inverse Fourier Transform

1. Oct 19, 2011

### cathode-ray

1. The problem statement, all variables and given/known data

Hi!

I tried to get the inverse fourier transform of the function:

$X(j\omega)=1/(jw+a)$​

for a>0, using the integral:

$x(t)=(1/2\pi)\int_{-\infty}^{+\infty} X(j\omega)e^{j\omega t}d\omega$​

I know that the inverse Fourier transform of $X(j\omega)$ is:

$x(t)=e^{-at}u(t), a>0$​

but when i tried to calculate the integral i got:

$x(t)=(1/2\pi)\int_{-\infty}^{+\infty} e^{j\omega t}/(jw+a)$​

,and i wasnt able to get that integral using any of the techniques i know. What am i doing wrong or isnt possible to get the inverse Fourier transform of that function this way?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 20, 2011

### susskind_leon

I guess you have to look into the residue theorem here. Let me know if you need more instructions.

3. Oct 24, 2011

### cathode-ray

Thanks a lot :D. I always forgot that theorem to calculate integrals. It should work. Im gonna try it and if i have some problem i will say something.