Jointly optimized high-order error feedback and realization for roundoff noise minimizaion in state-space digital filters

The joint optimization problem of high-order error feedback and realization for state-space digital filters to minimize the effects of roundoff noise at the filter output subject to l₂-scaling constraints is investigated. The problem is converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained optimization problem at hand 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 utility of the proposed technique.