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.