Signal Analysis And Estimation

This work introduces the analysis (using Fourier techniques) of continuous and discrete deterministic signals along with both estimation and spectral analysis of random signals. It is divided into two sections. Chapters 1-5 are devoted to the analysis of continuous and discrete deterministic signals, while Chapters 6-9 cover the properties, spectral analysis, and estimation of random signals. In addition, in order to assist readers, examples are liberally included throughout every chapter.

This book introduces readers to various signal processing models that have been used in analyzing periodic data, and discusses the statistical and computational methods involved. Signal processing can broadly be considered to be the recovery of information from physical observations. The received signals are usually disturbed by thermal, electrical, atmospheric or intentional interferences, and due to their random nature, statistical techniques play an important role in their analysis. Statistics is also used in the formulation of appropriate models to describe the behavior of systems, the development of appropriate techniques for estimation of model parameters and the assessment of the model performances. Analyzing different real-world data sets to illustrate how different models can be used in practice, and highlighting open problems for future research, the book is a valuable resource for senior undergraduate and graduate students specializing in mathematics or statistics.

"For those involved in the design and implementation of signal processing algorithms, this book strikes a balance between highly theoretical expositions and the more practical treatments, covering only those approaches necessary for obtaining an optimal estimator and analyzing its performance. Author Steven M. Kay discusses classical estimation followed by Bayesian estimation, and illustrates the theory with numerous pedagogical and real-world examples."--Cover, volume 1.

The purpose of this book is to explore several specific areas of research in two distinct but related fields: digital signal processing and modern control and estimation theory. There are enough similarities "and" differences in the philosophies, goals, and analytical techniques of the two fields to indicate that a concerted effort to understand these better might lead to some useful interaction and collaboration among researchers.The author writes that his examination "will in general not be result-oriented. Instead, I have been most interested in understanding the goals of the research and the methods and approach used. Understanding the goals may help us to see why the techniques used in the two disciplines differ. Inspecting the methods and approaches may allow one to see areas in which concepts in one field may be usefully applied in the other. The book undoubtedly has a control-oriented flavor, since it reflects the author's background and also since the original purpose of this study was to present a control theorist's point of view at the 1976 Arden House Workshop on Digital Signal Processing. However, an effort has been made to explore avenues in both disciplines in order to encourage researchers in the two fields to continue along these lines."Indeed, the book contains numerous suggestions for new research directions and speculations on possible new results, all of them a direct result of the purposeful mixing of the ideas of the two disciplines. For the benefit of researchers who may wish to follow up some of these suggestions and speculations, the author has assembled a comprehensive bibliography, consisting of more than 600 references.In order to achieve his unique perspective of viewing each field in the context of the other, the author examines such topics as stability analysis of feedback control systems and digital filters subject to the effects of finite wordlength arithmetic; linear prediction, parameter identification, and relationships involving Kalman filtering and "fast" algorithms; system synthesis, realization, and implementation; two-dimensional filtering, decentralized control and estimation, and some of their connections with image processing; and aspects of nonlinear system theory, including homomorphic and bilinear systems.

Signal processing may broadly be considered to involve the recovery of information from physical observations. The received signal is usually disturbed by thermal, electrical, atmospheric or intentional interferences. Due to the random nature of the signal, statistical techniques play an important role in analyzing the signal. Statistics is also used in the formulation of the appropriate models to describe the behavior of the system, the development of appropriate techniques for estimation of model parameters and the assessment of the model performances. Statistical signal processing basically refers to the analysis of random signals using appropriate statistical techniques. The main aim of this book is to introduce different signal processing models which have been used in analyzing periodic data, and different statistical and computational issues involved in solving them. We discuss in detail the sinusoidal frequency model which has been used extensively in analyzing periodic data occuring in various fields. We have tried to introduce different associated models and higher dimensional statistical signal processing models which have been further discussed in the literature. Different real data sets have been analyzed to illustrate how different models can be used in practice. Several open problems have been indicated for future research.

The techniques used for the extraction of information from received or ob served signals are applicable in many diverse areas such as radar, sonar, communications, geophysics, remote sensing, acoustics, meteorology, med ical imaging systems, and electronics warfare. The received signal is usually disturbed by thermal, electrical, atmospheric, channel, or intentional inter ferences. The received signal cannot be predicted deterministically, so that statistical methods are needed to describe the signal. In general, therefore, any received signal is analyzed as a random signal or process. The purpose of this book is to provide an elementary introduction to random signal analysis, estimation, filtering, and identification. The emphasis of the book is on the computational aspects as well as presentation of com mon analytical tools for systems involving random signals. The book covers random processes, stationary signals, spectral analysis, estimation, optimiz ation, detection, spectrum estimation, prediction, filtering, and identification. The book is addressed to practicing engineers and scientists. It can be used as a text for courses in the areas of random processes, estimation theory, and system identification by undergraduates and graduate students in engineer ing and science with some background in probability and linear algebra. Part of the book has been used by the author while teaching at State University of New York at Buffalo and California State University at Long Beach. Some of the algorithms presented in this book have been successfully applied to industrial projects.

This book embraces the many mathematical procedures that engineers and statisticians use to draw inference from imperfect or incomplete measurements. This book presents the fundamental ideas in statistical signal processing along four distinct lines: mathematical and statistical preliminaries; decision theory; estimation theory; and time series analysis.

Estimation theory is a product of need and technology. As a result, it is an integral part of many branches of science and engineering. To help readers differentiate among the rich collection of estimation methods and algorithms, this book describes in detail many of the important estimation methods and shows how they are interrelated. Written as a collection of lessons, this book introduces readers o the general field of estimation theory and includes abundant supplementary material.