Book description
Optimal filtering applied to stationary and nonstationary 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 nonstationary signals. Exercises with solutions feature in each chapter to demonstrate the practical application of these ideas using MATLAB.
Table of contents
 Cover
 Dedication
 Title Page
 Copyright
 Preface
 Introduction

Chapter 1. Random Vectors
 1.1. Definitions and general properties
 1.2. Spaces L1 (dP) and L2 (dP)
 1.3. Mathematical expectation and applications
 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
 Chapter 2. Gaussian Vectors
 Chapter 3. Introduction to Discrete Time Processes
 Chapter 4. Estimation
 Chapter 5. The Wiener Filter

Chapter 6. Adaptive Filtering: Algorithm of the Gradient and the LMS
 6.1. Introduction
 6.2. Position of problem [WID 85]
 6.3. Data representation
 6.4. Minimization of the cost function
 6.5. Gradient algorithm
 6.6. Geometric interpretation
 6.7. Stability and convergence
 6.8. Estimation of gradient and LMS algorithm
 6.9. Example of the application of the LMS algorithm
 6.10. Exercises for Chapter 6
 Chapter 7. The Kalman Filter
 Table of Symbols and Notations
 Bibliography
 Index
Product information
 Title: Discrete Stochastic Processes and Optimal Filtering, 2nd Edition
 Author(s):
 Release date: January 2010
 Publisher(s): Wiley
 ISBN: 9781848211810
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