Discrete stochastic processes and optimal filtering

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 fundamental feature in a range of applications, such as in navigation in aerospace and aeronautics, filter pro...

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Bibliographic Details
Main Author: Bertein, Jean-Claude
Other Authors: Ceschi, Roger
Format: eBook
Language:English
Published: London, U.K. ISTE 2010
Edition:2nd ed
Series:Digital signal and image processing series
Subjects:
Online Access:
Collection: O'Reilly - Collection details see MPG.ReNa
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245 0 0 |a Discrete stochastic processes and optimal filtering  |c Jean-Claude Bertein, Roger Ceschi 
250 |a 2nd ed 
260 |a London, U.K.  |b ISTE  |c 2010 
300 |a xii, 287 pages  |b illustrations 
505 0 |a 1.3.1. Definitions 1.3.2. Characteristic functions of a random vector ; 1.4. Second order random variables and vectors ; 1.5. Linear independence of vectors of L2 (dP) ; 1.6. Conditional expectation (concerning random vectors with density function) ; 1.7. Exercises for Chapter 1 
505 0 |a Chapter 2. Gaussian Vectors 2.1. Some reminders regarding random Gaussian vectors ; 2.2. Definition and characterization of Gaussian vectors ; 2.3. Results relative to independence ; 2.4. Affine transformation of a Gaussian vector ; 2.5. The existence of Gaussian vectors 
505 0 |a Includes bibliographical references and index 
505 0 |a 2.6. Exercises for Chapter 2 Chapter 3. Introduction to Discrete Time Processes ; 3.1. Definition ; 3.2. WSS processes and spectral measure ; 3.2.1. Spectral density ; 3.3. Spectral representation of a WSS process ; 3.3.1. Problem ; 3.3.2. Results 
505 0 |a 3.4. Introduction to digital filtering 3.5. Important example: autoregressive process ; 3.6. Exercises for Chapter 3 ; Chapter 4. Estimation ; 4.1. Position of the problem ; 4.2. Linear estimation ; 4.3. Best estimate -- conditional expectation 
505 0 |a Cover; Discrete Stochastic Processes and Optimal Filtering; Title Page; Copyright Page; Table of Contents; Preface ; Introduction ; Chapter 1. Random Vectors ; 1.1. Definitions and general properties ; 1.2. Spaces L1 (dP) and L2 (dP) ; 1.2.1. Definitions ; 1.2.2. Properties ; 1.3. Mathematical expectation and applications 
653 |a Stochastic processes / fast 
653 |a Processus stochastiques 
653 |a Traitement du signal / Mathématiques 
653 |a Signal processing / Mathematics 
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653 |a TECHNOLOGY & ENGINEERING / Signals & Signal Processing / bisacsh 
653 |a Digital filters (Mathematics) / fast 
653 |a COMPUTERS / Information Theory / bisacsh 
653 |a Filtres numériques (Mathématiques) 
653 |a Stochastic processes / http://id.loc.gov/authorities/subjects/sh85128181 
653 |a Signal processing / Mathematics / fast 
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520 |a 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 fundamental feature in a range of applications, such as in navigation in aerospace and aeronautics, filter processing in the telecommunications industry, etc. This book provides a comprehensive overview of this area, discussing random and Gaussian vectors, outlining the results necessary for the creation of Wiener and adaptive filters used for stationary signals, as well as examining Kalman filters which are used in relation to non-stationary signals. Exercises with solutions feature in each chapter to demonstrate the practical application of these ideas using MATLAB.