1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

F. transform problem

  1. Oct 29, 2011 #1
    1. The problem statement, all variables and given/known data

    Find Fourier transform of function

    [tex]f(x)=\frac{1}{x^2+a^2}[/tex], [tex]a>0[/tex]



    2. Relevant equations

    [tex]\mathcal{F}[\frac{1}{x^2+a^2}]=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}\frac{e^{-ikx}dx}{x^2+a^2}[/tex]



    3. The attempt at a solution

    Two different case

    [tex]k>0[/tex]

    and

    [tex]k<0[/tex]

    How to solve integral

    [tex]\mathcal{F}[\frac{1}{x^2+a^2}]=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}\frac{e^{-ikx}dx}{x^2+a^2}[/tex]

    Probably using complex analysis?! I forget this. I have two poles [tex]ia[/tex] and [tex]-ia[/tex]. How to integrate this? Is there some other method without using complex analysis?
     
  2. jcsd
  3. Oct 29, 2011 #2
    "Is there some other method without using complex analysis?"

    Nope. But complex analysis isn't that bad -- it just seems like black magic until you get used to it. You might want to look at the example at http://en.wikipedia.org/wiki/Residue_theorem .
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: F. transform problem
Loading...