1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: How to compute the 2D inverse Fourier transform?

  1. May 7, 2010 #1
    1. The problem statement, all variables and given/known data

    The problem is to obtain the inverse Fourier transform of the following 2D functions

    [tex]F(\mathbf{k})=\frac{k_{x}k_{y}}{k^{2}}[/tex]

    2. Relevant equations

    The relevant equations are the 2d Fourier transform formulas described http://fourier.eng.hmc.edu/e101/lectures/Image_Processing/node6.html" [Broken].

    3. The attempt at a solution

    [tex]\int d^{2}\mathbf{k}\,\frac{k_{x}k_{y}}{k^{2}}e^{i\mathbf{k}\cdot\mathbf{r}}&=&\int_{-\infty}^{+\infty}dp\int_{-\infty}^{+\infty}dq\,\frac{p q}{p^{2}+q^{2}}e^{ipx+iqy}[/tex]

    How would you proceed with the evaluation of this integral? I need some guidance on how to compute integrals like the above.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. May 8, 2010 #2

    lanedance

    User Avatar
    Homework Helper

    could you try polar co-ords?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook