More economical state-space digital-filter structures which are free of constant-input limit cycles

A theorem that establishes conditions for the elimination of constant-input limit cycles is used as the basis for a procedure for the synthesis of state-space structures. Three different second-order structures are obtained, and in each, granularity and overflow limit cycles can be eliminated under zero- and constant-input conditions. Detailed procedures are then presented for the application of one of the proposed structures to the design of parallel and cascade filters. The paper concludes with extensive comparisons which show that more economical low-noise and low-sensitivity state-space filter implementations are possible through the use of one of the proposed structures.