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partⅠ GENERAL INTRODUCTION 1

Objectives of PartⅠ 1

1 ADAPTIVE SYSTEMS 3

Definition and Characteristics 3

Areas of Application 4

General Properties 5

Open-and Closed-Loop Adaptation 6

Applications of Closed-Loop Adaptation 9

Example of an Adaptive System 11

The Chapters Ahead 13

2 THE ADAPTIVE LINEAR COMBINER 15

General Description 15

Input Signal and Weight Vectors 16

Desired Response and Error 18

The Performance Function 19

Gradient and Minimum Mean-Square Error 21

Example of a Performance Surface 22

Alternative Expression of the Gradient 24

Decorrelation of Error and Input Components 26

Exercises 26

partⅡ THEORY OF ADAPTATION WITH STATIONARY SIGNALS 31

Objectives of PartⅡ 31

3 PROPERTIES OF THE QUADRATIC PERFORMANCE SURFACE 33

Normal Form of the Input Correlation Matrix 34

Eigenvalues and Eigenvectors of the Input Correlation Matrix 34

An Example with Two Weights 36

Geometrical Significance of Eigenvectors and Eigenvalues 38

A Second Example 41

Exercises 43

4 SEARCHING THE PERFORMANCE SURFACE 46

Methods of Searching the Performance Surface 46

Basic Ideas of Gradient Search Methods 47

A Simple Gradient Search Algorithm and Its Solution 48

Stability and Rate of Convergence 49

The Learning Curve 51

Gradient Search by Newton's Method 52

Newton's Method in Multidimensional Space 54

Gradient Search by the Method of Steepest Descent 56

Comparison of Learning Curves 61

Exercises 63

5 GRADIENT ESTIMATION AND ITS EFFECTS ON ADAPTATION 66

Gradient Component Estimation by Derivative Measurement 66

The Performance Penalty 68

Derivative Measurement and Performance Penalties with Multiple Weights 69

Variance of the Gradient Estimate 71

Effects on the Weight-Vector Solution 75

Excess Mean-Square Error and Time Constants 80

Misadjustment 87

Comparative Performance of Newton's and Steepest-Descent Methods 89

Total Misadjustment and Other Practical Considerations 91

Exercises 93

partⅢ ADAPTIVE ALGORITHMS AND STRUCTURES 97

Objectives of PartⅢ 97

6 THE LMS ALGORITHM 99

Derivation of the LMS Algorithm 99

Convergence of the Weight Vector 101

An Example of Convergence 103

Learning Curve 107

Noise in the Weight-Vector Solution 109

Misadjustment 110

Performance 112

Exercises 114

7 THE z-TRANSFORM IN ADAPTIVE SIGNAL PROCESSING 117

The z-Transform 117

Right-and Left-Handed Sequences 119

Transfer Functions 120

Frequency Response 122

Impulse Response and Stability 124

The Inverse z-Transform 126

Correlation Functions and Power Spectra 128

The Performance Function 131

Examples of Performance Surfaces 134

Exercises 137

8 OTHER ADAPTIVE ALGORITHMS AND STRUCTURES 141

An Ideal:The LMS/Newton Algorithm 142

Properties of the LMS/Newton Algorithm 145

The Sequential Regression Algorithm 147

Adaptive Recursive Filters 154

Random-Search Algorithms 161

Lattice Structures 164

The Adaptive Lattice Predictor 173

Adaptive Filters with Orthogonal Signals 182

Exercises 186

partⅣ APPLICATIONS 193

Objectives of Part Ⅳ 193

9 ADAPTIVE MODELING AND SYSTEM IDENTIFICATION 195

General Description 195

Adaptive Modeling of a Multipath Communication Channel 200

Adaptive Modeling in Geophysieal Exploration 209

Adaptive Modeling in FIR Digital Filter Synthesis 212

Exercises 225

10 INVERSE ADAPTIVE MODELING,DECONVOLUTION,AND EQUALIZATION 231

General Description of Inverse Modeling 232

Some Theoretical Examples 236

Adaptive Equalization of Telephone Channels 244

Adapting Poles and Zeros for IIR Digital Filter Synthesis 250

Exercises 264

11 ADAPTIVE CONTROL SYSTEMS 270

Adaptive Model Control 271

Adaptive Inverse Control 280

Examples of Adaptive Inverse Control 285

Plant Noise and the Filtered-X LMS Algorithm 288

Inverse Control Using the Filtered-X LMS Algorithm 292

Model Reference Control 294

Exercises 298

12 ADAPTIVE INTERFERENCE CANCELING 302

Early Work in Adaptive Interference Canceling 303

The Concept of Adaptive Noise Canceling 303

Stationary Noise-Canceling Solutions 306

Effects of Signal Components in the Reference Input 311

The Adaptive Interference Canceler as a Notch Filter 316

The Adaptive Interference Canceler as a High-Pass Filter 323

Effects of Finite Length and Causality 324

Multiple-Reference Noise Canceling 327

Canceling 60-Hz Interference in Electrocardiography 329

Canceling Donor-Heart Interference in Heart-Transplant Electrocardiography 330

Canceling the Maternal ECG in Fetal Electrocardiography 334

Canceling Noise in Speech Signals 337

Canceling Echoes in Long-Distance Telephone Circuits 339

Canceling Antenna Sidelobe Interference 347

Canceling Periodic Interference with an Adaptive Predictor 349

The Adaptive Self-Tuning Filter 351

The Adaptive Line Enhancer 354

Conclusion 361

Exercises 361

13 INTRODUCTION TO ADAPTIVE ARRAYS AND ADAPTIVE BEAMFORMING 368

Sidelobe Cancellation 369

Beamforming with a Pilot Signal 383

Spatial Configurations 388

Adaptive Algorithms 391

Narrowband Experiments 394

Broadband Experiments 399

Exercises 404

14 ANALYSIS OF ADAPTIVE BEAMFORMERS 409

Performance Characteristics of Receiving Arrays 409

The Griffiths LMS Beamformer 412

The Frost Adaptive Beamformer 415

An Adaptive Beamformer with Poles and Zeros 420

Signal Cancellation and Distortion 429

Frequency-Hop Spread-Spectrum Techniques 442

Beamformers with Superresolution 445

Exercises 456

APPENDIX A A Portable Random Number Generator 459

INDEX 469