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Discrete stochastic processes and optimal filtering

This title is concerned with the founding principles of optimal filters. It proposes several reminders about both random vectors and Gaussian vectors. The study of discrete time processes makes it possible to tackle digital filtering; a chapter on estimation gives the principle results necessary for...

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Bibliographic Details
Main Authors: Bertein, Jean-Claude.
Corporate Authors: Wiley InterScience (Online service)
Group Author: Ceschi, Roger.
Published:
Literature type: Electronic eBook
Language: English
French
Subjects:
Signal processing > Mathematics.
Digital filters (Mathematics)
Stochastic processes.
Traitement du signal > Mathématiques.
Filtres numériques (Mathématiques)
Processus stochastiques.
COMPUTERS > Information Theory.
TECHNOLOGY & ENGINEERING > Signals & Signal Processing.
Electronic books.
Online Access: http://onlinelibrary.wiley.com/book/10.1002/9780470612293
Summary: This title is concerned with the founding principles of optimal filters. It proposes several reminders about both random vectors and Gaussian vectors. The study of discrete time processes makes it possible to tackle digital filtering; a chapter on estimation gives the principle results necessary for the construction of the Wiener filter and of the adaptive filter used in the case of stationary signals. It concludes with an examination of Kalman filtering which extends optimal filtering to the case of non-stationary signals. Exercises with solutions punctuate each chapter and practical examples are dealt with using Matlab software. This work is aimed at graduate students and engineers as well as members of the scientific community who wish to rediscover the founding principles of optimal filters.
Item Description: "First published in France in 2005 by Hermes Science/Lavoisier entitled "Processus stochastiques discrets et filtrages optimaux"."
Carrier Form: ix, 287 p. : ill. ; 24 cm.
Bibliography: Includes bibliographical references (p. [283]) and index.
ISBN: 9780470612293
0470612290
9781847046246 (electronic bk.)
184704624X (electronic bk.)
1280847859
9781280847851
Index Number: TK5102
CLC: TN911.72
Contents: Cover -- Table of Contents -- Preface -- Introduction -- Chapter 146; Random Vectors -- 146;146; Definitions and general properties -- 146;246; Spaces L140;dP41; and L240;dP41; -- 146;346; Mathematical expectation and applications -- 146;446; Second order random variables and vectors -- 146;546; Linear independence of vectors of L240;dP41; -- 146;646; Conditional expectation 40;concerning random vectors with -- 146;746; Exercises for Chapter 1 -- Chapter 246; Gaussian Vectors -- 246;146; Some reminders regarding random Gaussian vectors -- 246;246; Definition and characterization of Gaussian vectors -- 246;346; Results relative to independence -- 246;446; Affine transformation of a Gaussian vector -- 246;546; The existence of Gaussian vectors -- 246;646; Exercises for Chapter 2 -- Chapter 346; Introduction to Discrete Time Processes -- 346;146; Definition -- 346;246; WSS processes and spectral measure46; -- 346;346; Spectral representation of a WSS process -- 346;446; Introduction to digital filtering -- 346;546; Important example58; autoregressive process -- 346;646; Exercises for Chapter 3 -- Chapter 446; Estimation -- 446;146; Position of the problem -- 446;246; Linear estimation -- 446;346; Best estimate 8211; conditional expectation -- 446;446; Example58; prediction of an autoregressive process AR 40;141; -- 446;546; Multivariate processes -- 446;646; Exercises for Chapter 4 -- Chapter 546; The Wiener Filter -- 546;146; Introduction -- 546;246; Resolution and calculation of the FIR filter -- 546;346; Evaluation of the least error -- 546;446; Resolution and calculation of the IIR filter -- 546;546; Evaluation of least mean square error -- 546;646; Exercises for Chapter 5 -- Chapter 646; Adaptive Filtering58; Algorithm of the Gradient and the LMS46; -- 646;146; Introduction -- 646;246; Position of problem -- 646;346; Data representation -- 646;446; Minimization of the cost function -- 646;546; Gradient algorithm -- 646;646; Geometric interpretation -- 646;746; Stability and convergence -- 646;846; Estimation of gradient and LMS algorithm -- 646;946; Example of the application of the LMS algorithm46; -- 646;1046; Exercises for Chapter 6 -- Chapter 746; The Kalman Filter -- 746;146; Position of problem -- 746;246; Approach to estimation -- 746;346; Kalman filtering -- 746;446; Exercises for Chapter 7 -- Table of Symbols and Notations -- Bibliography -- Index -- Last Page.

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