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Fundamentals Adaptive systems are at the very core of modern digital signal processing. There are many reasons for this, foremost amongst these is that adaptive filtering, prediction or identification do not require explicit a priori statistical knowledge of the input data. Adaptive systems are employed in numerous areas such as biomedicine, communications, control, radar, sonar and video processing (Haykin 1996a). | Recurrent Neural Networks for Prediction Authored by Danilo P. Mandic Jonathon A. Chambers Copyright 2001 John Wiley Sons Ltd ISBNs 0-471-49517-4 Hardback 0-470-84535-X Electronic 2 Fundamentals Perspective Adaptive systems are at the very core of modern digital signal processing. There are many reasons for this foremost amongst these is that adaptive filtering prediction or identification do not require explicit a priori statistical knowledge of the input data. Adaptive systems are employed in numerous areas such as biomedicine communications control radar sonar and video processing Haykin 1996a . Chapter Summary In this chapter the fundamentals of adaptive systems are introduced. Emphasis is first placed upon the various structures available for adaptive signal processing and includes the predictor structure which is the focus of this book. Basic learning algorithms and concepts are next detailed in the context of linear and nonlinear structure filters and networks. Finally the issue of modularity is discussed. Adaptive Systems Adaptability in essence is the ability to react in sympathy with disturbances to the environment. A system that exhibits adaptability is said to be adaptive. Biological systems are adaptive systems animals for example can adapt to changes in their environment through a learning process Haykin 1999a . A generic adaptive system employed in engineering is shown in Figure . It consists of a set of adjustable parameters weights within some filter structure an error calculation block the difference between the desired response and the output of the filter structure a control learning algorithm for the adaptation of the weights. The type of learning represented in Figure is so-called supervised learning since the learning is directed by the desired response of the system. Here the goal 10 ADAPTIVE SYSTEMS is to adjust iteratively the free parameters weights of the adaptive system so as to minimise a prescribed cost function .