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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 infinite impulse response (IIR) filters and systems. In the liter- attire, two classes of methods are available for RN reduction or minimization-one uses state-space coordinate transformation, the other uses error feedback/feed-forward of state variables. In this paper, we propose a method for the joint optimization of error feedback/feed-forward 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. With the infinite-precision solution as a reference point, we then move on to derive a semidefinite programming (SDP) relaxation method for an approximate solution of optimal error-feedback matrix with sum-of-power-of-two entries under a given state-space realization. Simulations are presented to illustrate the proposed algorithms and demonstrate the performance of optimized systems. [ABSTRACT FROM AUTHOR]

Proposes a constrained optimization method for the design of basic and multistage frequency-response-masking (FRM) filters where the prototype filters are of infinite-impulse response (IIR) with prescribed pole radius. Overview of the proposed design; Alternatives offered by IIR FRM filters to its finite-impulse response counterpart in terms of filter performance; Overview of algorithms that can be used for solving general non-linear programming problems; Highlights of amplitude response of various filters.