Inverse Fourier Transform

  • #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 isnt possible to get the inverse Fourier transform of that function this way?

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
susskind_leon
179
0
I guess you have to look into the residue theorem here. Let me know if you need more instructions.
 
  • #3
cathode-ray
50
0
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.
 

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