Periodically Correlated Random Sequences
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Periodically Correlated Random Sequences
Uniquely combining theory, application, and computing, this book explores the spectral approach to time series analysis The use of periodically correlated (or cyclostationary) processes has become increasingly popular in a range of research areas such as meteorology, climate, communications, economics, and machine diagnostics. Periodically Correlated Random Sequences presents the main ideas of these processes through the use of basic definitions along with motivating, insightful, and illustrative examples. Extensive coverage of key concepts is provided, including second-order theory, Hilbert spaces, Fourier theory, and the spectral theory of harmonizable sequences. The authors also provide a paradigm for nonparametric time series analysis including tests for the presence of PC structures. Features of the book include: An emphasis on the link between the spectral theory of unitary operators and the correlation structure of PC sequences A discussion of the issues relating to nonparametric time series analysis for PC sequences, including estimation of the mean, correlation, and spectrum A balanced blend of historical background with modern application-specific references to periodically correlated processes An accompanying Web site that features additional exercises as well as data sets and programs written in MATLAB® for performing time series analysis on data that may have a PC structure Periodically Correlated Random Sequences is an ideal text on time series analysis for graduate-level statistics and engineering students who have previous experience in second-order stochastic processes (Hilbert space), vector spaces, random processes, and probability. This book also serves as a valuable reference for research statisticians and practitioners in areas of probability and statistics such as time series analysis, stochastic processes, and prediction theory.
Correlation Theory of Stationary and Related Random Functions
Author: A.M. Yaglom
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Correlation Theory of Stationary and Related Random Functions is an elementary introduction to the most important part of the theory dealing only with the first and second moments of these functions. This theory is a significant part of modern probability theory and offers both intrinsic mathematical interest and many concrete and practical applications. Stationary random functions arise in connection with stationary time series which are so important in many areas of engineering and other applications. This book presents the theory in such a way that it can be understood by readers without specialized mathematical backgrounds, requiring only the knowledge of elementary calculus. The first volume in this two-volume exposition contains the main theory; the supplementary notes and references of the second volume consist of detailed discussions of more specialized questions, some more additional material (which assumes a more thorough mathematical background than the rest of the book) and numerous references to the extensive literature.
Cyclostationarity: Theory and Methods
Author: Fakher Chaari
language: en
Publisher: Springer Science & Business Media
Release Date: 2014-01-16
In the last decade the research in signal analysis was dominated by models that encompass nonstationarity as an important feature. This book presents the results of a workshop held in Grodek—Poland in February 2013 which was dedicated to the investigation of cyclostationary signals. Its main objective is to highlight the strong interactions between theory and applications of cyclostationary signals with the use of modern statistical tools. An important application of cyclostationary signals is the analysis of mechanical signals generated by a vibrating mechanism. Cyclostationary models are very important to perform basic operations on signals in both time and frequency domains. One of the fundamental problems in diagnosis of rotating machine is the identification of significant modulating frequencies that contribute to the cyclostationary nature of the signals. The book shows that there are modern tools available for analyzing cyclostationary signals without the assumption of gaussianity. Those methods are based on the ideas of bootstrap, subsampling and Fraction-of-time (FOT) models. The book is organised in two parts. The first part will be dedicated to pure theory on cyclostationarity. Applications are presented in the second part including several mechanical systems such as bearings, gears, with or without damages.