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 J₀ transform (61-point and 120-point operators), and two for the Hankel J₁ 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.