Minimized roundoff noise and pole sensitivity subject to L2-Scaling constraints for IIR filters

Abstract

This paper investigates the minimization problem of weighted roundoff noise and pole sensitivity subject to l2-scaling constraints for state-space digital filters. A new measure for evaluating roundoff noise and pole sensitivity is proposed, and an efficient technique for minimizing this measure is developed. It is shown that the problem can be converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained optimization problem at hand is then solved iteratively by employing an efficient quasi-Newton algorithm with closed-form formulas for key gradient evaluation. Finally a numerical example is presented to demonstrate the validity and effectiveness of the proposed technique.