Adaptive filters

This chapter provides an introduction to adaptive signal processing, covering subjects ranging from basic principles to the most important advanced developments. After a brief example describing a typical application, we present an overview of how adaptive filters work, in which we use only deterministic arguments and concepts from basic linear systems theory, followed by a description of a few common applications of adaptive filters. Later, we turn to a more general model for adaptive filters based on stochastic processes and optimum estimation. Then three of the most important adaptive algorithms – LMS, NLMS, and RLS – are derived and analyzed in detail. The chapter closes with a brief description of some important extensions to the basic adaptive filtering algorithms and some promising research topics. Since adaptive filter theory brings together results from several fields, short reviews are provided for most of the necessary material in separate sections, which the reader may consult if needed.