A fading-memory system is a system that tends to forget its inputnasymptotically over time. It has been shown that discrete-timenfading-memory systems can be uniformly approximated arbitrarily closelynover a set of bounded input sequences simply by uniformly approximatingnsufficiently closely either the external or internal representation ofnthe system. In other words, the problem of uniformly approximating anfading-memory system reduces to the problem of uniformly approximatingncontinuous real-valued functions on compact sets. The perceptron is anparametric model that realizes a set of continuous real-valued functionsnthat is uniformly dense in the set of all continuous real-valuednfunctions. Using the perceptron to uniformly approximate the externalnand internal representations of a discrete-time fading-memory systemnresults, respectively, in simple finite-memory and infinite-memorynparametric system models. Algorithms for estimating the model parametersnthat yield a best approximation to a given fading-memory system arendiscussed. An application to nonlinear noise cancellation in telephonensystems is presented
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