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Lower limit cycle bounds for narrow transition band digital filters

A procedure for obtaining tighter bounds on zero-input limit cycles is presented. The determined new bounds are applicable to digital filters of arbitrary order described in state-space formulation and implemented with fixed-point arithmetic. In most filters, we obtain smaller bounds through this new algorithm easy to implement and to execute in a very short computer time. The bounds obtained for narrow transition band digital filters are far lower than those corresponding to classical procedures, yielding enormous computation savings to complete an exhaustive search. Simulation results are presented in different tables that show the validity of the proposed theory.