New digital linear filters for Hankel J₀ and J₁ transforms

Abstract

The numerical evaluation of certain integral transforms is required for the interpretation of some geophysical exploration data. Digital linear filter operators are widely used for carrying out such numerical integration.It is known that the method of Wiener-Hopf minimization of the error can be used to design very efficient, short digital linear filter operators for this purpose. We have found that, with appropriate modifications, this method can also be used to design longer filters. Two filters for the Hankel J 0 transform (61-point and 120-point operators), and two for the Hankel J 1 transform (47-point and 140-point operators) have been designed. For these transforms, the new filters give much lower errors compared to all other known filters of comparable, or somewhat longer, size. The new filter operators and some results of comparative performance tests with known integral transforms are presented.These filters would find widespread application in many numerical evaluation problems in geophysics. Figure 2. Relative errors of the new 61-point and 120-point J 0 filters, compared with errors of the 61-point J 0 filter given by Koefoed et al. (1972), marked Koef 61, the 283-point, singleprecision J 0 filter given by Anderson (1979), marked Ander 283, and the 801-point, double precision J 0 filter given by Anderson (1982), marked Ander 801, for the transform (4). Digital linear filters 755

Performance of Hankel transform filters for marine controlled-source electromagnetic surveys: a comparative study

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“…In general, the accuracy of the digital linear filter increases with filter length and sampling density (Guptasarma and Singh, 1997). Longer filters are expected to produce smaller errors and to be effective for a larger range of offset distances.…”

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“…Yet, it is known that the conventional approach to digital filter design relies on repeated usage of the sample domain Wiener-Hopf least-squares method within an optimization loop [18]. Since the computational cost of the Wiener-Hopf method is proportional to the square of the filter length, such multiple executions can take a huge amount of time for very long filter designs [17]. Thus, the accuracy of the result of computation can be theoretically enhanced by increasing the filter length, but at the cost of running an expensive optimization process.…”

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