Fast Hankel Transforms
نویسنده
چکیده
JOHANSEN, H. K., and SORENSEN, K., 1979, Fast Hankel Transforms, Geophysical Prospecting 27, 876-901. Inspired by the linear filter method introduced by D. P. Ghosh in rg7o we have developed a general theory for numerical evaluation of integrals of the Hankel type: m g(r) = Sf(A)hJ,(Ar)dh; v > I. II Replacing the usual sine interpolating function by sinsh (x) = a . sin (xx)/sinh (UTW), where the smoothness parameter u is chosen to be “small”, we obtain explicit series expansions for the sinsh-response or filter function H*. If the input function f(A exp (io)) is known to be analytic in the region o < A< CO, ) o 1 < wg of the complex plane, we can show that the absolute error on the output function is less than (K(wo)/r) . exp ( xw~/A), A being the logarthmic sampling distance. Due to the explicit expansions of H* the tails of the infinite summation 5 F(nA)H* -m ((WZ n)A) can be handled analytically. Since the only restriction on the order is v > I, the Fourier transform is a special case of the theory, v = & I/Z giving the sineand cosine transform, respectively. In theoretical model calculations the present method is considerably more efficient than the Fast Fourier Transform (FFT).
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