In Signal Processing, the concepts of frequency, which are usually referred to as “spectral” concepts, are omnipresent. The transition from analogue methods to the use of digital tools in spectral analysis was first achieved by simple adaptation of the classical analogue tools that had long been used previously. However, beyond the simple quest of methods with better frequency resolution, it has been possible to develop specific digital tools based on parametric modeling. This book deals with these parametric methods, first discussing those based on time series models, Capon’s method and its variants, and then estimators based on the notions of sub-spaces. However, the book also deals with the traditional “analogue” methods, now called non-parametric methods, which are still the most widely used in practical spectral analysis.
The book contains 9 chapters classified into three parts. Part I discusses tools for spectral analysis, which includes Chapters 1-4. Chapter 1, written by F. Castanié, discusses classes and representations of signals and gives a brief introduction of later chapters. Chapter 2, written by É. Le Carpentier, is devoted to digital signal processing. Important concepts are dealt with in great details, particularly in the case of the Fourier transform. Chapter 3, written by O. Besson and A. Ferrari, discusses estimation in spectral analysis. It provides the necessary material for the statistical analysis of various estimators (either of spectrum or of frequencies) in this book. Chapter 4, written by F. Castanié, covers time-series models including linear models (stationary or non-stationary), exponential models and non-linear models. Part II contributes to non-parametric methods, which only contains one chapter, i.e., Chapter 5 written by É. Le Carpentier. It begins with a brief introduction and then discusses methods for estimating the power spectral density via filter bank methods for the analysis of continuous time signals and periodogram method and its variants for the analysis of discrete time signals). A generalization to higher order spectra is also given there. Part III is devoted to parametric methods, which contains Chapters 6-9. Chapter 6, written by C. Maihes and F. Castanié, discusses spectral analysis by stationary times series modelling. It presents the various parametric models of stationary processes including the ARMA and Prony models. Chapter 7, written by N. Martin, is regarding minimum variance. It introduces Capon’s method and its variants. Chapter 8, written by S. Marcos, is devoted to sub-space based estimators. It covers the MUSIC method, MinNorm method, “linear” subspace method and the ESPRIT method. Chapter 9, written by C. Mailhes and F. Castanié, contributes to the spectral analysis of random non-stationary signals. It gives the definition of “evolutive spectrum”, tackles the non-parametric tech niques, and creates a panorama of the parametric methods used in a non-stationary context.
This book is intended for researchers who are working in the area of signal processing.