Statistical spectral analysis : a nonprobabilistic theory

This book presents a general theory and methodology for empirical spectral analysis. The treatment is original because it does not make use of the difficult concept of ergodicity to provide a link between the empirical methods and the abstract probabilistic theory of stochastic processes. Instead, it shows that all the concepts and methods of empirical spectral analysis can be explained in a more straightforward fashion in terms of a deterministic theory: a theory based on time-averages of a single time-series rather than ensemble-averages of hypothetical random samples from an abstract probabilistic model. Specifically, the fundamental concepts and methods of empirical spectral analysis are explained without use of probability calculus. This approach is in keeping with the profound and influential work of Norbert Wiener in his classic paper Generalized Harmonic Analysis published in 1930. Part I of this book is intended to serve as both a graduatelevel textbook and a technical reference. The only prerequisite is an introductory course on Fourier analysis. However, some prior exposure to probability and statistics would be helpful. Part I presents a thorough development of fundamental concepts and results in the theory of statistical spectral analysis of empirical time-series from constant phenomena. The approach given here is one that will be helpful to students, for