FLOATING-POINT ROUNDOFF ERRORS OF SECOND-ORDER STATE-SPACE DIGITAL FIL TERS

摘要

An expression for the output roundoff error variance of second-order state-space digital filter implemented in floating-point arithmetic is derived. The expression is further specified to white-noise and constant inputs which are common in feedback systems. Numerical results are presented for four typical realizations, i.e., controller and observer canonical forms, balanced realization, and minimum- noise-gain filter. All possible realizations are examined by means of a parametric approach. It is demonstrated that a simple modal realization involving poles and residues of the filter transfer func- tion generates error not much larger than that of the minimum-noise-gain realization.