Periodically Correlated Random Sequences
Periodically Correlated Random Sequences

Author: Harry L. Hurd

Publisher: John Wiley & Sons

Published: 2007-11-09

Total Pages: 384

ISBN-13: 9780470182826

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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
Correlation Theory of Stationary and Related Random Functions

Author: A.M. Yaglom

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 267

ISBN-13: 1461246288

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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
Cyclostationarity: Theory and Methods

Author: Fakher Chaari

Publisher: Springer Science & Business Media

Published: 2014-01-16

Total Pages: 189

ISBN-13: 3319041878

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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.

Nonstationary Systems: Theory and Applications
Nonstationary Systems: Theory and Applications

Author: Fakher Chaari

Publisher: Springer Nature

Published: 2021-07-21

Total Pages: 439

ISBN-13: 3030821102

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This book offers an overview of current and recent methods for the analysis of the nonstationary processes, focusing on cyclostationary systems that are ubiquitous in various application fields. Based on the 13th Workshop on Nonstationary Systems and Their Applications, held on February 3-5, 2020, in Grodek nad Dunajcem, Poland, the book merges theoretical contributions describing new statistical and intelligent methods for analyzing nonstationary processes, and applied works showing how the proposed methods can be implemented in practice and do perform in real-world case studies. A significant part of the book is dedicated to nonstationary systems applications, with a special emphasis on those in condition monitoring.

Cyclostationary Processes and Time Series
Cyclostationary Processes and Time Series

Author: Antonio Napolitano

Publisher: Academic Press

Published: 2019-10-24

Total Pages: 628

ISBN-13: 0081027370

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Many processes in nature arise from the interaction of periodic phenomena with random phenomena. The results are processes that are not periodic, but whose statistical functions are periodic functions of time. These processes are called cyclostationary and are an appropriate mathematical model for signals encountered in many fields including communications, radar, sonar, telemetry, acoustics, mechanics, econometrics, astronomy, and biology. Cyclostationary Processes and Time Series: Theory, Applications, and Generalizations addresses these issues and includes the following key features. - Presents the foundations and developments of the second- and higher-order theory of cyclostationary signals - Performs signal analysis using both the classical stochastic process approach and the functional approach for time series - Provides applications in signal detection and estimation, filtering, parameter estimation, source location, modulation format classification, and biological signal characterization - Includes algorithms for cyclic spectral analysis along with Matlab/Octave code - Provides generalizations of the classical cyclostationary model in order to account for relative motion between transmitter and receiver and describe irregular statistical cyclicity in the data

Cyclostationarity: Theory and Methods III
Cyclostationarity: Theory and Methods III

Author: Fakher Chaari

Publisher: Springer

Published: 2017-02-25

Total Pages: 261

ISBN-13: 3319514458

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This book gathers contributions presented at the 9th Workshop on Cyclostationary Systems and Their Applications, held in Gródek nad Dunajcem, Poland in February 2016. It includes both theory-oriented and practice-oriented chapters. The former focus on heavy-tailed time series and processes, PAR models, rational spectra for PARMA processes, covariance invariant analysis, change point problems, and subsampling for time series, as well as the fraction-of-time approach, GARMA models and weak dependence. In turn, the latter report on case studies of various mechanical systems, and on stochastic and statistical methods, especially in the context of damage detection. The book provides students, researchers and professionals with a timely guide to cyclostationary systems, nonstationary processes and relevant engineering applications.

Generalizations of Cyclostationary Signal Processing
Generalizations of Cyclostationary Signal Processing

Author: Antonio Napolitano

Publisher: John Wiley & Sons

Published: 2012-12-07

Total Pages: 452

ISBN-13: 1118437918

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The relative motion between the transmitter and the receiver modifies the nonstationarity properties of the transmitted signal. In particular, the almost-cyclostationarity property exhibited by almost all modulated signals adopted in communications, radar, sonar, and telemetry can be transformed into more general kinds of nonstationarity. A proper statistical characterization of the received signal allows for the design of signal processing algorithms for detection, estimation, and classification that significantly outperform algorithms based on classical descriptions of signals.Generalizations of Cyclostationary Signal Processing addresses these issues and includes the following key features: Presents the underlying theoretical framework, accompanied by details of their practical application, for the mathematical models of generalized almost-cyclostationary processes and spectrally correlated processes; two classes of signals finding growing importance in areas such as mobile communications, radar and sonar. Explains second- and higher-order characterization of nonstationary stochastic processes in time and frequency domains. Discusses continuous- and discrete-time estimators of statistical functions of generalized almost-cyclostationary processes and spectrally correlated processes. Provides analysis of mean-square consistency and asymptotic Normality of statistical function estimators. Offers extensive analysis of Doppler channels owing to the relative motion between transmitter and receiver and/or surrounding scatterers. Performs signal analysis using both the classical stochastic-process approach and the functional approach, where statistical functions are built starting from a single function of time.

Cyclostationarity: Theory and Methods - II
Cyclostationarity: Theory and Methods - II

Author: Fakher Chaari

Publisher: Springer

Published: 2015-04-15

Total Pages: 210

ISBN-13: 3319163302

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This book reports on the latest advances in the analysis of non-stationary signals, with special emphasis on cyclostationary systems. It includes cutting-edge contributions presented at the 7th Workshop on “Cyclostationary Systems and Their Applications,” which was held in Gródek nad Dunajcem, Poland, in February 2014. The book covers both the theoretical properties of cyclostationary models and processes, including estimation problems for systems exhibiting cyclostationary properties, and several applications of cyclostationary systems, including case studies on gears and bearings, and methods for implementing cyclostationary processes for damage assessment in condition-based maintenance operations. It addresses the needs of students, researchers and professionals in the broad fields of engineering, mathematics and physics, with a special focus on those studying or working with nonstationary and/or cyclostationary processes.

Cyclostationarity: Theory and Methods – IV
Cyclostationarity: Theory and Methods – IV

Author: Fakher Chaari

Publisher: Springer

Published: 2019-07-31

Total Pages: 234

ISBN-13: 3030225291

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This book gathers contributions presented at the 10th Workshop on Cyclostationary Systems and Their Applications, held in Gródek nad Dunajcem, Poland in February 2017. It includes twelve interesting papers covering current topics related to both cyclostationary and general non stationary processes. Moreover, this book, which covers both theoretical and practical issues, offers a practice-oriented guide to the analysis of data sets with non-stationary behavior and a bridge between basic and applied research on nonstationary processes. It provides students, researchers and professionals with a timely guide on cyclostationary systems, nonstationary processes and relevant engineering applications.