Effects of input-scaling on the asymptotic overflow-stability properties of second-order recursive digital filters

This paper examines the stability properties of a second-order recursive digital filter having different overflow nonlinearities. Three new sets of sufficiency conditions have been derived to ensure asymptotic stability of the filter with respect to various admissible classes of input signals under different input-scaling conditions. Using these criteria, various regions of stability in the coefficient plane have been computed as a function of the input scale factor
c
. Examples of a filter's responses illustrate the dependence of the stability property of the forced response on the input-scaling conditions.