Separate/joint optimization of error feedback and realization for roundoff noise minimization in a class of 2-D state-space digital filters

Techniques for the separate/joint optimization of error-feedback and realization are developed to minimize the roundoff noise subject to l ₂-norm dynamic-range scaling constraints for a class of 2-D state-space digital filters. In the joint optimization, the problem at hand is converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained problem obtained is then solved by applying an efficient quasi-Newton algorithm. A numerical example is presented to illustrate the utility of the proposed techniques.