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**Adaptive signal processing.**
*(English)*
Zbl 0593.93063

Prentice-Hall Signal Processing Series. Englewood Cliffs, N.J.: Prentice- Hall, Inc. XVIII, 474 p. $ 63.40 (1985).

This book is a basic text on adaptive processing and recursive estimation of parameters in linear discrete-time systems. The prerequisites necessary to understand this text are minimal, which makes it useful for introducing the unexperienced student to the field.

The book is divided into four main parts. The first three parts, which contain 8 chapters (about 190 pages) present the basic theory of adaptation with stationary signals and of the adaptive algorithms. The fourth part consists of 6 chapters (about 260 pages) on various engineering applications of adaptive signal processing.

The following are the theoretical chapters: Chap. 1. Adaptive systems (contains basic definitions and general properties of adaptation); Chap. 2. The adaptive linear combiner (introduces the linear regression model structure that will be used throughout the book, and also describes the least-squares (LS) criterion for estimating the parameters in such models); Chap. 3. Properties of the quadratic performance surface (presents basic algebraic results on quadratic forms); Chap. 4. Searching the performance surface (presents the gradient and Newton methods for surfaces with exactly known first- and second-order derivatives, and describes their behavior on quadratic surfaces); Chap. 5. Gradient estimation and its effects on adaptation (relaxes the assumption of Ch. 4 that the gradient vector and possibly the Hessian matrix can be exactly determined); Chap. 6. The LMS algorithm [introduces the least-mean-square (LMS) algorithm (which could also be called a stochastic gradient algorithm), and establishes its convergence properties under certain conditions); Chap. 7. The z-transform in adaptive signal processing (reviews basic facts about the z-transform, transfer functions, frequency responses and power spectra); Chap. 8. Other adaptive algorithms and structures (introduces the sequential regression algorithm (perhaps better known as the on-line LS algorithm, extends the LMS algorithm to pole-zero systems; presents random search algorithms, adaptive lattice structures and adaptive filters with orthogonal signals).

The remaining chapters cover the major applications of adaptive signal processing. Their titles should be self-explanatory. Chap. 9. Adaptive modeling and system identification; Chap. 10. Inverse adaptive modeling, deconvolution, and equalization; Chap. 11. Adaptive control systems; Chap. 12. Adaptive interference cancelling; Chap. 13. Introduction to adaptive arrays and adaptive beam forming; and Chap. 14. Analysis of adaptive beam formers.

The book also contains many exercises (some of which are computer oriented) and an appendix describing a portable random number generator.

The book is divided into four main parts. The first three parts, which contain 8 chapters (about 190 pages) present the basic theory of adaptation with stationary signals and of the adaptive algorithms. The fourth part consists of 6 chapters (about 260 pages) on various engineering applications of adaptive signal processing.

The following are the theoretical chapters: Chap. 1. Adaptive systems (contains basic definitions and general properties of adaptation); Chap. 2. The adaptive linear combiner (introduces the linear regression model structure that will be used throughout the book, and also describes the least-squares (LS) criterion for estimating the parameters in such models); Chap. 3. Properties of the quadratic performance surface (presents basic algebraic results on quadratic forms); Chap. 4. Searching the performance surface (presents the gradient and Newton methods for surfaces with exactly known first- and second-order derivatives, and describes their behavior on quadratic surfaces); Chap. 5. Gradient estimation and its effects on adaptation (relaxes the assumption of Ch. 4 that the gradient vector and possibly the Hessian matrix can be exactly determined); Chap. 6. The LMS algorithm [introduces the least-mean-square (LMS) algorithm (which could also be called a stochastic gradient algorithm), and establishes its convergence properties under certain conditions); Chap. 7. The z-transform in adaptive signal processing (reviews basic facts about the z-transform, transfer functions, frequency responses and power spectra); Chap. 8. Other adaptive algorithms and structures (introduces the sequential regression algorithm (perhaps better known as the on-line LS algorithm, extends the LMS algorithm to pole-zero systems; presents random search algorithms, adaptive lattice structures and adaptive filters with orthogonal signals).

The remaining chapters cover the major applications of adaptive signal processing. Their titles should be self-explanatory. Chap. 9. Adaptive modeling and system identification; Chap. 10. Inverse adaptive modeling, deconvolution, and equalization; Chap. 11. Adaptive control systems; Chap. 12. Adaptive interference cancelling; Chap. 13. Introduction to adaptive arrays and adaptive beam forming; and Chap. 14. Analysis of adaptive beam formers.

The book also contains many exercises (some of which are computer oriented) and an appendix describing a portable random number generator.

Reviewer: P.Stoica

### MSC:

93E12 | Identification in stochastic control theory |

93-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory |

93C40 | Adaptive control/observation systems |

60G35 | Signal detection and filtering (aspects of stochastic processes) |

62F35 | Robustness and adaptive procedures (parametric inference) |

62J05 | Linear regression; mixed models |

62L20 | Stochastic approximation |

93B30 | System identification |

94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |

93E10 | Estimation and detection in stochastic control theory |

93E25 | Computational methods in stochastic control (MSC2010) |