On the stability of the forced response of digital filters with overflow nonlinearities

The forced response of a general type of digital filter, implemented with overflow nonlinearities, is studied. A definition of stability of this forced response is given. It is indicated that this stability can be studied by means of the zero-input behavior of a system, with the same structure but with time-varying nonlinearities. A theorem is derived giving sufficient conditions for the stability of the forced response of a digital system. Some results of the application of this theorem to wave digital filters are given.