The definition and development of a modified discrete describing function, referred to as dual input discrete describing function, is considered. High-frequency signal is injected into the nonlinearity to quench the limit cycles in closed-loop autonomous relay-type sampled-data systems. An analytic procedure is described, which aims at deriving the dual input discrete describing function for a relay in the Z domain. Copyright © 1969 by The Institute of Electrical and Electronics Engineers, Inc.