Discrete Stochastic Processes and Optimal Filtering, 2nd Edition

Table of Contents

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

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

2.6. Exercises for Chapter 2

Chapter 3. Introduction to Discrete Time Processes

3.1. Definition

3.2. WSS processes and spectral measure

3.3. Spectral representation of a WSS process

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

4.4. Example: prediction of an autoregressive process AR (1)

4.5. Multivariate processes

4.6. Exercises for Chapter 4

Chapter 5. The Wiener Filter

5.1. Introduction

5.2. Resolution and calculation of the FIR filter

5.3. Evaluation of the least error

5.4. Resolution and calculation of the IIR filter

5.5. Evaluation of least mean square error

5.6. Exercises for Chapter 5

Chapter 6. Adaptive Filtering: Algorithm of the Gradient and the ...