Spectral analysis for physical applications. Multitaper and conventional univariate techniques.

*(English)*Zbl 0796.62077
Cambridge: Cambridge University Press,. xxvii, 583 p. (1993).

This book starts with an introduction to spectral analysis (Chapter 1) which illustrates and motivates the key ideas of the subject matter by means of simple examples. Chapter 2 contains a brief review of the theory of stationary stochastic processes. In Chapter 3 the authors prepare the ground for stochastic spectral analysis by reviewing, in a detailed and fairly self-contained manner, the concepts and properties related to various spectra of deterministic functions or sequences. Chapter 4 deals with the foundations of stochastic spectral analysis, starting with the Cramér spectral representation of a stationary process, whereas Chapter 5 reviews material on linear time-invariant filters with stationary stochastic processes as inputs. Spectral estimation methods make the subject of Chapters 6 through 10. Nonparametric (periodogram-based) spectral estimation is discussed in Chapter 6, and multitaper spectral estimation in the next two chapters. Chapter 9 is concerned with parametric (mostly AR-based) spectral estimation and, finally, line spectral analysis is dealt with in Chapter 10.

The book contains end-of-chapter exercises for the (graduate) student as well as a rather detailed subject index. The software used to produce the numerical examples has been made available by the authors on Internet. The book is well-written and it may find a niche in the literature as an intermediate text between more rigorous mathematically-oriented texts and practically-oriented engineering books.

The book contains end-of-chapter exercises for the (graduate) student as well as a rather detailed subject index. The software used to produce the numerical examples has been made available by the authors on Internet. The book is well-written and it may find a niche in the literature as an intermediate text between more rigorous mathematically-oriented texts and practically-oriented engineering books.

Reviewer: P.Stoica (Bucureşti)

##### MSC:

62M15 | Inference from stochastic processes and spectral analysis |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

62N99 | Survival analysis and censored data |

62P99 | Applications of statistics |