TY - JOUR

T1 - The Identification of Nonlinear Discrete-Time Fading-Memory Systems Using Neural Network Models

AU - Matthews, Michael B.

AU - Moschytz, George S.

PY - 1994/11

Y1 - 1994/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0028550651&partnerID=8YFLogxK

U2 - 10.1109/82.331544

DO - 10.1109/82.331544

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AN - SCOPUS:0028550651

SN - 1057-7130

VL - 41

SP - 740

EP - 751

JO - IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing

JF - IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing

IS - 11

ER -