Expansions for discrete-time nonlinear systems

Results are given concerning the existence and other properties of Volterra-like input-output expansions for discrete-time systems whose inputs and outputs are defined on the time set {0,1,2,...}. The results, which establish the existence of (and show how to obtain) a locally convergent input-output expansion for a very large class of systems, are along the lines of those reported recently by this writer for continuous-time systems. With regard to one of the theorems given here, new ground is broken in that the theorem directly addresses the case where the nonlinear part of the system need not be assumed to be memoryless. Systems of the kind considered arise, for example, in the area of communication channel modeling for digital data transmission.