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2D FT of f(r): Fast Hankel Transforms

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  • Subject: [mg64157] 2D FT of f(r): Fast Hankel Transforms
  • From: "Hypermars" <hypermars at>
  • Date: Thu, 2 Feb 2006 19:09:09 -0500 (EST)
  • Sender: owner-wri-mathgroup at

Are Fast (or the so-called quasi-Fast) Hankel Transforms implemented or
implementable in Mathematica?

Two-dimensional Fourier Transforms of functions f[r] where r=Sqrt[x^2+y^2]
are actually one-dimensional Hankel Transforms of order zero. So I was
wondering if one could use somehow 1D FFTs to optimize 2D FTs of f[r].

What I do now is rather lame:

Fourier[ Table[ f[ Sqrt[i^2+j^2] ],{j,-n/2+1,n/2},{i,-n/2+1,n/2}] ]

and I would like something similar to

FHT[ Table[ f[i],{i,n} ] ]

to have directly the radially symmetric 2D spectrum.



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