Digital Spectral Analysis

Digital Spectral Analysis offers a broad perspective of spectral estimation techniques and their implementation. Coverage includes spectral estimation of discrete-time or discrete-space sequences derived by sampling continuous-time or continuous-space signals. The treatment emphasizes the behavior of each spectral estimator for short data records and provides over 40 techniques described and available as implemented MATLAB functions. In addition to summarizing classical spectral estimation, this text provides theoretical background and review material in linear systems, Fourier transforms, matrix algebra, random processes, and statistics. Topics include Prony's method, parametric methods, the minimum variance method, eigenanalysis-based estimators, multichannel methods, and two-dimensional methods. Suitable for advanced undergraduates and graduate students of electrical engineering — and for scientific use in the signal processing application community outside of universities — the treatment's prerequisites include some knowledge of discrete-time linear system and transform theory, introductory probability and statistics, and linear algebra. 1987 edition.

This user guide serves as a companion to Digital Spectral Analysis, Second Edition (Dover Publications, 2019), illustrating all the text's techniques and algorithms, plus time versus frequency analysis. The spectral demonstrations use MATLAB software that encompasses the full experience from inputting signal sources, interactively setting technique parameters and processing with those parameters, and choosing from a variety of plotting techniques to display the results. The processing functions and scripts have been coded to automatically handle sample data that is either real-valued or complex-valued, permitting the user to simply modify the demonstration scripts to input their own data for analysis. Four integrated software categories support the demonstrations. These are the main MATLAB spectral demonstration scripts, supporting MATLAB plotting scripts, MATLAB processing functions listed in this guide, and signal sample data sources. Scripts and demonstration data files can be found on the Dover website for free downloading; see the Introduction for details.

Digital Spectral Analysis provides a single source that offers complete coverage of the spectral analysis domain. This self-contained work includes details on advanced topics that are usually presented in scattered sources throughout the literature. The theoretical principles necessary for the understanding of spectral analysis are discussed in the first four chapters: fundamentals, digital signal processing, estimation in spectral analysis, and time-series models. An entire chapter is devoted to the non-parametric methods most widely used in industry. High resolution methods are detailed in a further four chapters: spectral analysis by stationary time series modeling, minimum variance, and subspace-based estimators. Finally, advanced concepts are the core of the last four chapters: spectral analysis of non-stationary random signals, space time adaptive processing: irregularly sampled data processing, particle filtering and tracking of varying sinusoids. Suitable for students, engineers working in industry, and academics at any level, this book provides a rare complete overview of the spectral analysis domain.

This book covers the basics of processing and spectral analysis of monovariate discrete-time signals. The approach is practical, the aim being to acquaint the reader with the indications for and drawbacks of the various methods and to highlight possible misuses. The book is rich in original ideas, visualized in new and illuminating ways, and is structured so that parts can be skipped without loss of continuity. Many examples are included, based on synthetic data and real measurements from the fields of physics, biology, medicine, macroeconomics etc., and a complete set of MATLAB exercises requiring no previous experience of programming is provided. Prior advanced mathematical skills are not needed in order to understand the contents: a good command of basic mathematical analysis is sufficient. Where more advanced mathematical tools are necessary, they are included in an Appendix and presented in an easy-to-follow way. With this book, digital signal processing leaves the domain of engineering to address the needs of scientists and scholars in traditionally less quantitative disciplines, now facing increasing amounts of data.

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 “analog” methods, now called non-parametric methods, which are still the most widely used in practical spectral analysis.

This user guide serves as a companion to Digital Spectral Analysis, Second Edition (Dover Publications, 2019), illustrating all the text's techniques and algorithms, plus time versus frequency analysis. The spectral demonstrations use MATLAB software that encompasses the full experience from inputting signal sources, interactively setting technique parameters and processing with those parameters, and choosing from a variety of plotting techniques to display the results. The processing functions and scripts have been coded to automatically handle sample data that is either real-valued or complex-valued, permitting the user to simply modify the demonstration scripts to input their own data for analysis. Four integrated software categories support the demonstrations. These are the main MATLAB spectral demonstration scripts, supporting MATLAB plotting scripts, MATLAB processing functions listed in this guide, and signal sample data sources. Scripts and demonstration data files can be found on the Dover website for free downloading; see the Introduction for details.