FAST HANKEL TRANSFORMS*
H. K. JOHANSEN, Kai Sørensen · Geophysical Prospecting · 1979
A bstract Inspired by the linear filter method introduced by D. P. Ghosh in 1970 we have developed a general theory for numerical evaluation of integrals of the Hankel type: image Replacing the usual sine interpolating function by sinsh ( x ) = a · sin (ρ x )/sinh ( a ρ x ), where the smoothness parameter a is chosen to be “small”, we obtain explicit series expansions for the sinsh‐response or filter function H *. If the input function f (λ exp (iω)) is known to be analytic in the region o − 1, the Fourier transform is a special case of the theory, ν=± 1/2 giving the sine‐ and cosine transform, respectively. In theoretical model calculations the present method is considerably more efficient than the Fast Fourier Transform (FFT).