Relationship between input-scaling and stability of the forced response of recursive digital filters

The stability of forced response of a general recursive digital filter operating in the inherent presence of overflow nonlinearities is examined. A theorem is derived that relates forced-response stability to the degree of input-scaling. The technique is applied to the investigation of the stability properties of state-space digital filters, resulting in a criterion for the forced-input stability of Nth-order state-space filters. Subsequently, it is applied to the second-order case. The resultant stability criterion is applied to the investigation of optimal state-space and normal filters. Finally, the stability properties of wave digital filters are discussed.<
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