Book description
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.
Table of contents
- Cover Page
- Title Page
- Copyright
- Dedication
- Table of Contents
- Preface
- Introduction
-
Chapter 1: Random Vectors
- 1.1. Definitions and general properties
- 1.2. Spaces L 1 ( dP ) and L 2 ( dP )
- 1.3. Mathematical expectation and applications
- 1.4. Second order random variables and vectors
- 1.5. Linear independence of vectors of L 2 ( 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
- Author(s):
- Release date: May 2007
- Publisher(s): Wiley
- ISBN: 9781905209743
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