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Volume 27 Number 4
  • E-ISSN: 1365-2478

Abstract

A

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:

Replacing the usual sine interpolating function by sinsh () =· sin (ρ)/sinh (ρ), where the smoothness parameter is chosen to be “small”, we obtain explicit series expansions for the sinsh‐response or filter function *.

If the input function (λ exp (iω)) is known to be analytic in the region o < λ < ∞, |ω|≤ω of the complex plane, we can show that the absolute error on the output function is less than ((ω)/) · exp (−ρω/Δ), Δ being the logarthmic sampling distance.

Due to the explicit expansions of * the tails of the infinite summation

((−)Δ) can be handled analytically.

Since the only restriction on the order is ν > − 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).

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2006-04-27
2024-04-19

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  • Article Type: Research Article

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