THE IDENTIFICATION OF NONLINEAR DISCRETE-TIME FADING-MEMORY SYSTEMS USING NEURAL-NETWORK MODELS

A fading-memory system is a system that tends to forget its input asym ptotically over time. It has been shown that discrete-time fading-memo ry systems can be uniformly approximated arbitrarily closely over a se t of bounded input sequences simply by uniformly approximating suffici ently closely either the external or internal representation of the sy stem. In other words, the problem of uniformly approximating a fading- memory system reduces to the problem of uniformly approximating contin uous real-valued functions on compact sets. The perceptron is a parame tric model that realizes a set of continuous real-valued functions tha t is uniformly dense in the set of all continuous real-valued function s. Using the perceptron to uniformly approximate the external and inte rnal representations of a discrete-time fading-memory system results, respectively, in simple finite-memory and infinite-memory parametric s ystem models. Algorithms for estimating the model parameters that yiel d a best approximation to a given fading-memory system are discussed. An application to nonlinear noise cancellation in telephone systems is presented.