Improved Digital Filters for Evaluating Fourier and Hankel Transform Integrals.

摘要

New algorithms are described for evaluating Fourier (cosine,sine) and Hankel (J sub 0,J sub 1) transform integrals by means of digital filters. The filters have been designed with extended lengths so that a variable convolution operation can be applied to a large class of integral transforms having the same system transfer function. A lagged-convolution method is also presented to significantly decrease the computation time when computing a series of like-transforms over a parameter set spaced the same as the filters. Accuracy of the new filters is comparable to Gaussian integration,provided moderate parameter ranges and well-behaved kernel functions are used. A collection of Fortran 4subprograms is included for both real and complex functions for each flter type. The algorithms have been successfully used in geophysical applications containing a wide variety of integral transforms.