Design data for digital Butterworth filters in geophysical data processing

Abstract

The analysis of geophysical data by computer often includes post-processing with digital filters. Of particular interest are those digital filters which approximate ideal low pass, high pass, band pass or band reject responses. Design data are presented for digital filters which approximate a Butterworth response. Low pass, high pass, band pass and band reject filters are discussed and it is shown that in general the nth order low pass Butterworth transfer function may be factorised with the denominator consisting of linear and/or quadratic factors. Simple frequency transformations permit the realisation of the associated high pass, band pass and band reject transfer functions for these factors. Application of the bilinear transformation yields the z transforms for these factors which, when used recursively, provide the desired filter response. Fortran computer programs are included and the performance limitations of the digital filters are illustrated by comparison with some ideal Butterworth responses.