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Fourier Help

  • To: mathgroup at
  • Subject: [mg43648] Fourier Help
  • From: Arnold Gregory Civ AFRL/SNAT <Gregory.Arnold at>
  • Date: Sat, 27 Sep 2003 04:58:10 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

I'm working with ver 5 & I've found a strange feature of the FourierTransform.  I was trying to reproduce the following transformation pair in Mathematica:

FourierTransform[(1 - Sign[-1 + x1^2 + x2^2])/2,{x1,x2},{k1,k2}]=
(2*Pi*BesselJ[1, Sqrt[k1^2 + k2^2]] ) / Sqrt[k1^2 + k2^2]

Basically, this is a unit disk centered at the origin.  I've tried representing it as a unit step, too with no differences obtained.  Mathematica 5 yields a strange mixed & incomplete (wrong?!?) result:

{Sqrt[Pi/2]*DiracDelta[k1] - 
  Sqrt[Pi/2]*DiracDelta[k1]*Sign[-1 + x1^2 + x2^2], 
 Sqrt[Pi/2]*DiracDelta[k2] - 
  Sqrt[Pi/2]*DiracDelta[k2]*Sign[-1 + x1^2 + x2^2]}

Notice that this is a list with 2 terms!?!  And a function of both the x's and k's?!?   The 1D version of this works (I didn't check it), but it didn't specifically return the bessel function.

Mathematica  4.2 returned the original input with some error notations.

Does anybody know of a more complete set of transform tables and / or a simple workaround. Obviously I could encode this particular transform directly, but if somebody else has already fixed this & other transforms I'm likely to need...

Thanks for any help & insight you can provide,


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