Jointly optimal high-order error feedback and realization for roundoff noise minimization in 2-D state-space digital filters

The joint optimization problem of high-order error feedback and realization for minimizing roundoff noise at filter output subject to l
₂
-scaling constraints is investigated for two-dimensional (2-D) state-space digital filters. Linear algebraic techniques that convert the problem at hand into an unconstrained optimization problem are explored, and an efficient quasi-Newton algorithm is then applied to solve the unconstrained optimization problem iteratively. In this connection, closed-form formulas are derived for fast and accurate gradient evaluation. Finally a numerical example is presented to illustrate the validity and effectiveness of the proposed algorithm.