A sufficient condition for absence of overflow oscillations in arbitrary digital filters based on the element equations

Arbitrary digital filters are uniquely described by the element equations proposed here in which the outputs of adders and multipliers are defined as variables in addition to state variables. Equations of overflow oscillations in arbitrary digital filters are represented using the simultaneous equations or the DFT. A sufficient condition for absence of overflow oscillations is obtained by means of the element equations and the second method of Liapunov, and is applied to a ladder form as an example.