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Inverse Fourier Transform

  1. Oct 19, 2011 #1
    1. The problem statement, all variables and given/known data

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



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 20, 2011 #2
    I guess you have to look into the residue theorem here. Let me know if you need more instructions.
     
  4. Oct 24, 2011 #3
    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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