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Trying to invert an expression

  1. May 26, 2015 #1
    I've come across an expression that looks like

    n(k) = ∫cos(x-y)f(x,y)dxdy

    Is there a name for this transform? I would like to invert it to obtain f(x,y) but I'm not used to the 2D integral on the RHS. I tried to turn it into a fourier transform:

    n(k) = 1/2 ( ∫eixe-iyf(x,y)dxdy + ∫e-ixeiyf(x,y)dxdy)

    but got stuck. Any help would be appreciated.

    Thanks
     
  2. jcsd
  3. May 27, 2015 #2

    Ssnow

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    Hi, there is something of strange, where is ##k## in the integral?, you say ##n(k)## but in the right side I don't see ##k##, and what is the domain of integration ?
     
  4. May 27, 2015 #3
    You are right! Sorry, I forgot about the k when writing down the expression(s). The correct expression is

    n(k) = ∫ cos( k(x-y) ) f(x,y) dxdy

    Thanks
     
  5. May 27, 2015 #4

    Ssnow

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    I think your transform is analogous to the ''cosine transform'', I hope you can find something useful here

    http://dsp-book.narod.ru/TAH/ch03.pdf

    but I think (as you wrote...) it is possible to use the inverse Fourier transform...
     
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