Adaptive Filter Theory

The primary aim of this book is to develop the mathematical theory of various realizations of linear adaptive filters. Adaptation is accomplished by adjusting the free para meters (coefficients) of a filter in accordance with the input data, which, in reality, makes the adaptive filter nonlinear. When we speak of an adaptive filter being “linear,” we mean the following: The input-output map of the filter obeys the principle of superposition whenever, at any particular instant of time, the filter’s parameters are all fixed. There is no unique solution to the linear adaptive filtering problem. Rather, we have a “kit of tools” represented by a variety of recursive algorithms, each of which offers desirable features of its own. This book provides such a kit. In terms of background, it is assumed that the reader has taken introductory undergraduate courses on probability theory and digital signal processing; undergraduate courses on communication and control systems would also be an advantage.