Jointly optimal error feedforward, high-order error feedback and realization for roundoff noise minimization in IIR digital filters

Joint optimization of error feedforward, high-order error feedback and state-space realization for minimizing roundoff noise at filter output subject to l₂-scaling constraints for state-space digital filters is investigated. Linear algebraic techniques that convert the problems 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 demonstrate that the high-order error feedback does offer much improved performance and that the proposed joint optimization is superior relative to a sequentially optimized system where the state-space coordinate transformation as well as error feedforward and high-order error feedback matrices are optimized separately.