Comments on: Covariance–Invariant Digital Filtering–A Better Digital Processing Technique for Ground Motion Studies; by J. E. Ehrenberg and E. N. Hernandez

Abstract

Ehrenberg and Hernandez (1981) have presented a novel recursive digital algorithm for computing the relative displacement of a single degree-of-freedom linear oscillator subjected to a digitized ground motion record. Their stated aim is to achieve an accurate and numerically efficient algorithm which will allow the displacement response spectrum at several oscillator frequencies to be computed in real time by a microprocessor system. They compare their algorithm, the "covariance-invariant filter" with the "bilinear z filter" proposed by Stagner and Hart (1970), and show that the new algorithm gives better accuracy for a given ratio fs/fn, where fs and fn are the sample and oscillator frequencies, respectively, and that the improvement in relative accuracy becomes greater as f~/fn is decreased. Alternatively, for a given accuracy and oscillator frequency, the ground motion can be sampled at a lower rate for their algorithm, thereby ensuring it is more efficient computationally than the bilinear z filter.