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Fourier transform.

  1. Apr 8, 2008 #1
    1. The problem statement, all variables and given/known data
    I need to take the inverse Fourier transform of


    2. Relevant equations


    It might be useful that [tex]\frac{2b}{\pi(x^2+b^2)}=\frac{1}{b+ix}+\frac{1}{b-ix}[/tex]

    3. The attempt at a solution
    I know the result is [tex]e^{(-b|t|)}[/tex], and I can get from [tex]e^{(-b|t|)}[/tex] to
    [tex]\frac{b}{\pi(x^2+b^2)}[/tex], but how do I do it in reverse if I didn't already know the pair existed? This doesn't require complex integration does it?
    Last edited: Apr 8, 2008
  2. jcsd
  3. Apr 9, 2008 #2
    I have to admit my first thought was a contour integral...

    In my experience, things involving |x| tend to require them.
  4. Apr 9, 2008 #3


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    It is a standard contour integral. Close the contour with a semicircle above the real axis.
  5. Apr 9, 2008 #4
    Okay guys, thanks, that is what I was thinking, but the book I'm in doesn't have anything else involving complex integration, so I assumed that I was just missing a trick.
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