Roundoff Noise Minimization for a Class of 2-D State-Space Digital Filters Using Joint Optimization of High-Order Error Feedback and Realization

Abstract

For two-dimensional IIR digital filters described by the Fornasini-Marchesini second model, the problem of jointly optimizing high-order error feedback and realization to minimize the effects of roundoff noise at the filter output subject to l₂-scaling constraints is investigated. The problem at hand is converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained optimization problem is then solved iteratively by applying an efficient quasi-Newton algorithm with closed-form formulas for key gradient evaluation. Finally, a numerical example is presented to illustrate the validity and effectiveness of the proposed technique.