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
> 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".
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