The Identification of Nonlinear Discrete-Time Fading-Memory Systems Using Neural Network Models

Michael B. Matthews, George S. Moschytz

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


A fading-memory system is a system that tends to forget its input asymptotically over time. It has been shown that discrete-time fading-memory systems can be uniformly approximated arbitrarily closely over a set of bounded input sequences simply by uniformly approximating sufficiently closely either the external or internal representation of the system. In other words, the problem of uniformly approximating a fading-memory system reduces to the problem of uniformly approximating continuous real-valued functions on compact sets. The perceptron is a parametric model that realizes a set of continuous real-valued functions that is uniformly dense in the set of all continuous real-valued functions. Using the perceptron to uniformly approximate the external and internal representations of a discrete-time fading-memory system results, respectively, in simple Unite-memory and infinite-memory parametric system models. Algorithms for estimating the model parameters that yield a best approximation to a given fading-memory system are discussed. An application to nonlinear noise cancellation in telephone systems is presented.

Original languageEnglish
Pages (from-to)740-751
Number of pages12
JournalIEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing
Issue number11
StatePublished - Nov 1994
Externally publishedYes


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