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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?
     
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