Jointly optimized error-feedback and realization for roundoff noise minimization in state-space digital filters

Roundoff noise (RN) is known to exist in digital filters and systems under finite-precision operations and can become a critical factor for severe performance degradation in IIR filters and systems. Two classes of methods are available for RN reduction or minimization - one uses state-space coordinate transformation, the other uses error feedback of state variables. In this paper, we propose a method for the joint optimization of error feedback and state-space realization. It is shown that the problem at hand can be solved in an unconstrained optimization setting. With a closed-form formula for gradient evaluation and an efficient quasi-Newton solver, the unconstrained minimization problem can be solved efficiently.