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

• To: mathgroup at smc.vnet.net
• Subject: [mg64165] RE: [mg64157] 2D FT of f(r): Fast Hankel Transforms
• From: "David Annetts" <davidannetts at aapt.net.au>
• Date: Fri, 3 Feb 2006 01:03:52 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

> 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].

You can implement them as a convolution with a digital filter.  Google for
various papers so you can derive coefficients, but one I'd recommend is
JOHANSEN, HK, AND SORENSEN, K. Fast Hankel transforms in Geophysical
Prospecting from a "fair while ago".

Regards,

Dave.