Weighted Minimization of Roundoff Noise and Pole Sensitivity Subject to l₂-Scaling Constraints for State-Space Digital Filters

Abstract

This paper deals with the problem of minimizing roundoff noise and pole sensitivity simultaneously subject to l₂-scaling constraints for state-space digital filters. A novel measure for evaluating roundoff noise and pole sensitivity is proposed, and an efficient technique for minimizing this measure by jointly optimizing state-space realization and error feedback is explored, namely, the constrained optimization problem at hand is converted into an unconstrained problem and then the resultant problem is solved by employing a quasi-Newton algorithm. A numerical example is presented to demonstrate the validity and effectiveness of the proposed technique.