Roundoff noise minimization of state-space digital filters using separate and joint error feedback/coordinate transformation optimization

This paper investigates the problem of minimizing roundoff noise under l₂-norm dynamic-range scaling constraints in state-space digital fibers by means of error feedback as well as joint error feedback/coordinate transformation optimization. First, several techniques, for the determination of optimal full-scale, diagonal, and scalar error-feedback matrices for a given state-space digital filter are proposed, where three realization schemes, namely, the general state-space realization, input-balanced realization, and optimal realization in the sense of Hwang-Mullis-Roberts are examined. Furthermore, an iterative approach is developed for jointly optimizing a scalar error-feedback matrix and a coordinate transformation matrix so as to minimize the roundoff noise subject to the l₂-norm dynamic-range scaling constraints. The proposed method may be regarded as an alternative, but much simpler and more general, approach to Hwang´s method for synthesizing the optimal filter structure with minimum roundoff noise. A case study is included to illustrate the utility of the proposed techniques.