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Improved digital filters for evaluating Fourier and Hankel transform integrals

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Abstract

New algorithms are described for evaluating Fourier (cosine, sine) and Hankel (J0,J1) 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 f' 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 IV subprograms is included for both real and complex functions for each filter type. The algorithms have been successfully used in geophysical applications containing a wide variety of integral transforms

Additional Publication Details

Publication type:
Report
Publication Subtype:
USGS Unnumbered Series
Title:
Improved digital filters for evaluating Fourier and Hankel transform integrals
Year Published:
1975
Language:
English
Publisher:
U.S. Geological Survey
Publisher location:
Denver, CO
Description:
119 p.
Additional Online Files(Y/N):
N