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Discrete stochastic processes and optimal filtering

Author: Jean-Claude Bertein; Roger Ceschi; Wiley InterScience (Online service)
Publisher: Newport Beach, CA : ISTE USA, 2007.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Bertein, Jean-Claude.
Discrete stochastic processes and optimal filtering.
Newport Beach, CA : ISTE USA, 2007
(DLC) 2007009433
(OCoLC)85830758
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jean-Claude Bertein; Roger Ceschi; Wiley InterScience (Online service)
ISBN: 9780470612293 0470612290 9781847046246 184704624X 1280847859 9781280847851
OCLC Number: 520990378
Notes: "First published in France in 2005 by Hermes Science/Lavoisier entitled "Processus stochastiques discrets et filtrages optimaux"."
Description: 1 online resource (ix, 287 pages) : illustrations
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.
Other Titles: Processus stochastiques discrets et filtrages optimaux.
Responsibility: Jean-Claude Bertein, Roger Ceschi.
More information:

Abstract:

Optimal filtering applied to stationary and non-stationary signals provides the most efficient means of dealing with problems arising from the extraction of noise signals. Moreover, it is a  Read more...

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