The Theory Of Linear Prediction
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The Theory Of Linear Prediction
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Author : P. P. Vaidyanathan
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2008
The Theory Of Linear Prediction written by P. P. Vaidyanathan and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Of Properties Relating to Levinson's Recursion.
The Theory Of Linear Prediction
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Author : P.P. Vaidyanathan
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
The Theory Of Linear Prediction written by P.P. Vaidyanathan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Technology & Engineering categories.
Linear prediction theory has had a profound impact in the field of digital signal processing. Although the theory dates back to the early 1940s, its influence can still be seen in applications today. The theory is based on very elegant mathematics and leads to many beautiful insights into statistical signal processing. Although prediction is only a part of the more general topics of linear estimation, filtering, and smoothing, this book focuses on linear prediction. This has enabled detailed discussion of a number of issues that are normally not found in texts. For example, the theory of vector linear prediction is explained in considerable detail and so is the theory of line spectral processes. This focus and its small size make the book different from many excellent texts which cover the topic, including a few that are actually dedicated to linear prediction. There are several examples and computer-based demonstrations of the theory. Applications are mentioned wherever appropriate, but the focus is not on the detailed development of these applications. The writing style is meant to be suitable for self-study as well as for classroom use at the senior and first-year graduate levels. The text is self-contained for readers with introductory exposure to signal processing, random processes, and the theory of matrices, and a historical perspective and detailed outline are given in the first chapter. Table of Contents: Introduction / The Optimal Linear Prediction Problem / Levinson's Recursion / Lattice Structures for Linear Prediction / Autoregressive Modeling / Prediction Error Bound and Spectral Flatness / Line Spectral Processes / Linear Prediction Theory for Vector Processes / Appendix A: Linear Estimation of Random Variables / B: Proof of a Property of Autocorrelations / C: Stability of the Inverse Filter / Recursion Satisfied by AR Autocorrelations
Stationary Processes And Prediction Theory
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Author : Harry Furstenberg
language : en
Publisher: Princeton University Press
Release Date : 1960-08-21
Stationary Processes And Prediction Theory written by Harry Furstenberg and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960-08-21 with Mathematics categories.
The description for this book, Stationary Processes and Prediction Theory. (AM-44), Volume 44, will be forthcoming.
Linear Model Theory
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Author : Dale L. Zimmerman
language : en
Publisher: Springer Nature
Release Date : 2020-11-02
Linear Model Theory written by Dale L. Zimmerman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-02 with Mathematics categories.
This textbook presents a unified and rigorous approach to best linear unbiased estimation and prediction of parameters and random quantities in linear models, as well as other theory upon which much of the statistical methodology associated with linear models is based. The single most unique feature of the book is that each major concept or result is illustrated with one or more concrete examples or special cases. Commonly used methodologies based on the theory are presented in methodological interludes scattered throughout the book, along with a wealth of exercises that will benefit students and instructors alike. Generalized inverses are used throughout, so that the model matrix and various other matrices are not required to have full rank. Considerably more emphasis is given to estimability, partitioned analyses of variance, constrained least squares, effects of model misspecification, and most especially prediction than in many other textbooks on linear models. This book is intended for master and PhD students with a basic grasp of statistical theory, matrix algebra and applied regression analysis, and for instructors of linear models courses. Solutions to the book’s exercises are available in the companion volume Linear Model Theory - Exercises and Solutions by the same author.
Linear Circuits
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Author : Nagai
language : en
Publisher: CRC Press
Release Date : 1989-11-27
Linear Circuits written by Nagai and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-11-27 with Technology & Engineering categories.
This book documents the significant progress in studies concerning linear circuits and systems, including their applications to digital filters, in Japan. It considers rational approximations in circuit and system theory and deals with the digital lattice filters used in digital signal processing.
Linear Prediction Theory
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Author : Peter Strobach
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Linear Prediction Theory written by Peter Strobach and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Lnear prediction theory and the related algorithms have matured to the point where they now form an integral part of many real-world adaptive systems. When it is necessary to extract information from a random process, we are frequently faced with the problem of analyzing and solving special systems of linear equations. In the general case these systems are overdetermined and may be characterized by additional properties, such as update and shift-invariance properties. Usually, one employs exact or approximate least-squares methods to solve the resulting class of linear equations. Mainly during the last decade, researchers in various fields have contributed techniques and nomenclature for this type of least-squares problem. This body of methods now constitutes what we call the theory of linear prediction. The immense interest that it has aroused clearly emerges from recent advances in processor technology, which provide the means to implement linear prediction algorithms, and to operate them in real time. The practical effect is the occurrence of a new class of high-performance adaptive systems for control, communications and system identification applications. This monograph presumes a background in discrete-time digital signal processing, including Z-transforms, and a basic knowledge of discrete-time random processes. One of the difficulties I have en countered while writing this book is that many engineers and computer scientists lack knowledge of fundamental mathematics and geometry.
Plane Answers To Complex Questions
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Author : Ronald Christensen
language : en
Publisher: Springer Science & Business Media
Release Date : 1996
Plane Answers To Complex Questions written by Ronald Christensen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This textbook provides a wide-ranging introduction to the use of linear models in analyzing data. The author's emphasis is on providing a unified treatment of the analysis of variance models and regression models by presenting a vector space and projections approach to the subject. Every chapter comes with numerous exercises and examples, which will make it ideal for a graduate-level course on this subject.
Prediction And Regulation By Linear Least Square Methods
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Author : Peter Whittle
language : en
Publisher:
Release Date : 1983
Prediction And Regulation By Linear Least Square Methods written by Peter Whittle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
Prediction and Regulation by Linear Least-Square Methods was first published in 1963. This revised second edition was issued in 1983. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions.During the past two decades, statistical theories of prediction and control have assumed an increasing importance in all fields of scientific research. To understand a phenomenon is to be able to predict it and to influence it in predictable ways. First published in 1963 and long out of print, Prediction and Regulation by Linear Least-Square Methods offers important tools for constructing models of dynamic phenomena. This elegantly written book has been a basic reference for researchers in many applied sciences who seek practical information about the representation and manipulation of stationary stochastic processes. Peter Whittle’s text has a devoted group of readers and users, especially among economists. This edition contains the unchanged text of the original and adds new works by the author and a foreword by economist Thomas J. Sargent.
Linear Processes In Function Spaces
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Author : Denis Bosq
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Linear Processes In Function Spaces written by Denis Bosq and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces. The necessary mathematical tools are presented in Chapters 1 and 2. Chapters 3 to 6 deal with autoregressive processes in Hilbert and Banach spaces. Chapter 7 is devoted to general linear processes and Chapter 8 with statistical prediction. Implementation and numerical applications appear in Chapter 9. The book assumes a knowledge of classical probability theory and statistics. Denis Bosq is Professor of Statistics at the University of Paris 6 (Pierre et Marie Curie). He is Chief-Editor of Statistical Inference for Stochastic Processes and of Annales de l'ISUP, and Associate Editor of the Journal of Nonparametric Statistics. He is an elected member of the International Statistical Institute, and he has published about 100 papers or works on nonparametric statistics and five books including Nonparametric Statistics for Stochastic Processes: Estimation and Prediction, Second Edition (Springer, 1998).
Foundations Of Time Series Analysis And Prediction Theory
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Author : Mohsen Pourahmadi
language : en
Publisher: John Wiley & Sons
Release Date : 2001-06-01
Foundations Of Time Series Analysis And Prediction Theory written by Mohsen Pourahmadi and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-01 with Mathematics categories.
Foundations of time series for researchers and students This volume provides a mathematical foundation for time seriesanalysis and prediction theory using the idea of regression and thegeometry of Hilbert spaces. It presents an overview of the tools oftime series data analysis, a detailed structural analysis ofstationary processes through various reparameterizations employingtechniques from prediction theory, digital signal processing, andlinear algebra. The author emphasizes the foundation and structureof time series and backs up this coverage with theory andapplication. End-of-chapter exercises provide reinforcement for self-study andappendices covering multivariate distributions and Bayesianforecasting add useful reference material. Further coveragefeatures: * Similarities between time series analysis and longitudinal dataanalysis * Parsimonious modeling of covariance matrices through ARMA-likemodels * Fundamental roles of the Wold decomposition andorthogonalization * Applications in digital signal processing and Kalmanfiltering * Review of functional and harmonic analysis and predictiontheory Foundations of Time Series Analysis and Prediction Theory guidesreaders from the very applied principles of time series analysisthrough the most theoretical underpinnings of prediction theory. Itprovides a firm foundation for a widely applicable subject forstudents, researchers, and professionals in diverse scientificfields.