- #1
cathode-ray
- 50
- 0
Homework Statement
Hi!
I tried to get the inverse Fourier transform of the function:
[itex]X(j\omega)=1/(jw+a)[/itex]
for a>0, using the integral:
[itex]x(t)=(1/2\pi)\int_{-\infty}^{+\infty} X(j\omega)e^{j\omega t}d\omega[/itex]
I know that the inverse Fourier transform of [itex]X(j\omega)[/itex] is:
[itex]x(t)=e^{-at}u(t), a>0[/itex]
but when i tried to calculate the integral i got:
[itex]x(t)=(1/2\pi)\int_{-\infty}^{+\infty} e^{j\omega t}/(jw+a)[/itex]
,and i wasnt able to get that integral using any of the techniques i know. What am i doing wrong or isn't possible to get the inverse Fourier transform of that function this way?