自适应滤波器原理 英文版 第3版PDF电子书下载

Introduction 1

1．The Filtering Problem 1

2．Adaptive Filters 2

3．Linear Filter Structures 4

4．Approaches to the Development of Linear Adaptive Filtering Algorithms 9

Contents 13

Preface 13

5．Real and Complex Forms of Adaptive Filters 14

6．Nonlinear Adaptive Filters 15

Acknowledgments 16

7．Applications 18

8．Some Historical Notes 67

PART 1 BACKGROUND MATERIAL 78

Chapter 1 Discrete-Time Signal Processing 79

1.1 z-Transform 79

1.2 Linear Time-Invariant Filters 81

1.3 Minimum-Phase Filters 86

1.4 Discrete Fourier Transform 87

1.5 Implementing Convolutions Using the DFT 87

1.6 Discrete Cosine Transform 93

1.7 Summary and Discussion 94

Problems 95

Chapter 2 Stationary Processes and Models 96

2.1 Partial Characterization of a Discrete-Time Stochastic Process 97

2.2 Mean Ergodic Theorem 98

2.3 Correlation Matrix 100

2.4 Correlation Matrix of Sine Wave Plus Noi se 106

2.5 Stochastic Models 108

2.6 Wold Decomposition 115

2.7 Asymptotic Stationarity of an Autoregressive Process 116

2.8 Yule-Walker Equations 118

2.9 Computer Experiment:Autoregressive Process of Order 2 120

2.10 Selecting the Model Order 128

2.11 Complex Gaussian Processes 130

2.12 Summary and Discussion 132

Problems 133

Chapter 3 Spectrum Analysis 136

3.1 Power Spectral Density 136

3.2 Properties of Power Spectral Density 138

3.3 Transmission of a Stationary Process Through a Linear Filter 140

3.4 Cramér Spectral Representation for a Stationary Process 144

3.5 Power Spectrum Estimation 146

3.6 Other Statistical Characteristics of a Stochastic Process 149

3.7 Polyspectra 150

3.8 Spectral-Correlation Density 154

3.9 Summary and Discussion 157

Problems 158

4.1 The Eigenvalue Problem 160

Chapter 4 Eigenanalysis 160

4.2 Properties of Eigenvalues and Eigenvectors 162

4.3 Low-Rank Modeling 176

4.4 Eigenfilters 181

4.5 Eigenvalue Computations 184

4.6 Summary and Discussion 187

Problems 188

PART 2 LINEAR OPTIMUM FILTERING 193

Chapter 5 Wiener Filters 194

5.1 Linear Optimum Filtering:Problem Statement 194

5.2 Principle of Orthogonality 197

5.3 Minimum Mean-Squared Error 201

5.4 Wiener-Hopf Equations 203

5.5 Error-Performance Surface 206

5.6 Numerical Example 210

5.7 Channel Equalization 217

5.8 Linearly Constrained Minimum Variance Filter 220

5.9 Generalized Sidelobe Cancelers 227

5.10 Summary and Disussion 235

Problems 236

Chapter 6 Linear Prediction 241

6.1 Forward Linear Prediction 242

6.2 Backward Linear Prediction 248

6.3 Levinson-Durbin Algorithm 254

6.4 Properties of Prediction-Error Filters 262

6.5 Schur-Cohn Test 271

6.6 Autoregressive Modeling of a Stationary Stochastic Process 273

6.7 Cholesky Factorization 276

6.8 Lattice Predictors 280

6.9 Joint-Process Estimation 286

6.10 Block Estimation 290

6.11 Summary and Discussion 293

Problems 295

Chapter 7 Kalman Filters 302

7.1 Recursive Minimum Mean-Square Estimation for Scalar Random Variables 303

7.2 Statement of the Kalman FiItering Problem 306

7.3 The Innovations Process 307

7.4 Estimation ofthe State using the Innovations Process 310

7.5 Filtering 317

7.6 Initial Conditions 320

7.7 Summary of the Kalman FiIter 320

7.8 Variants of the Kalman Filter 322

7.9 The Extended Kalman Filter 328

7.10 Summary and Discussion 333

Problems 334

PART 3 LINEAR ADAPTIVE FILTERING 338

8.1 Some Preliminaries 339

Chapter 8 Method of Steepest Descent 339

8.2 Steepest-Descent Algorithm 341

8.3 Stability of the Steepest-Descent Algorithm 343

8.4 Example 350

8.5 Summary and Discussion 362

Problems 362

Chapter 9 Least-Mean-Square Algorithm 365

9.1 Overview of the Structure and Operation of the Least-Mean-Square Algorithm 365

9.2 Least-Mean-Square Adaptation Algorithm 367

9.3 Examples 372

9.4 Stability and Performance Analysis of the LMS Algodthm 390

9.5 Summary of the LMS Algorithm 405

9.6 Computer Experiment on Adaptive Prediction 406

9.7 Computer Experiment on Adaptive Equalization 412

9.8 Computer Experiment on Minimum-Variance Distortionless Response Beamformer 421

9.9 Directionality of Convergence of the LMS Algorithm for Non-White Inputs 425

9.10 Robustness of the LMS Algorithm 427

9.11 Normalized LMS Algorithm 432

9.12 Summary and Discussion 438

Problems 439

Chapter 10 Frequency-Domain Adaptive Filters 445

10.1 Block Adaptive Filters 446

10.2 Fast LMS Algorithm 451

10.3 Unconstrained Frequency-Domain Adaptive Filtering 457

10.4 Self-Orthogonalizing Adaptive Filters 458

10.5 Computer Experiment on Adaptive Equalization 469

10.6 Classification ofAdaptive Filtering Algorithms 477

10.7 Summary and Discussion 478

Problems 479

Chapter 11 Method of Least Squares 483

11.1 Statement of the Linear Least-Squares Estimation Problem 483

11.2 Data Windowing 486

11.3 Principle of Orthogonality(Revisited) 487

11.4 Minimum Sum ofError Squares 491

11.5 Normal Equations and Linear Least-Squares Filters 492

11.6 Time-Averaged Correlation Matrix 495

11.7 Reformulation of the Normal Equations in Terms of Data Matrices 497

11.8 Properties of Least-Squares Estimates 502

11.9 Parametric Spectrum Estimation 506

11.10 Singular Value Decomposition 516

11.11 Pseudoinverse 524

11.12 Interpretation of Singular Values and Singular Vectors 525

11.13 Minimum Norm Solution to the Linear Least-Squares Problem 526

11.14 Normalized LMS Algorithm Viewed as the Minimum-Norm Solution to anUnderdetermined Least-Squares Estimation Problem 530

11.5 Summary and Discussion 532

Problems 533

Chapter 12 Rotations and Reflections 536

12.1 Plane Rotations 537

12.2 Two-Sided Jacobi Algorithm 538

12.3 Cyclic Jacobi Algorithm 544

12.4 Householder Transformation 548

12.5 The QR Algorithm 551

12.6 Summary and Discussion 558

Problems 560

Chapter 13 Recursive Least-Squares Algorithm 562

13.1 Some Preliminaries 563

13.2 The Matrix Inversion Lemma 565

13.3 The Exponentially Weighted Recursive Least-Squares Algorithm 566

13.4 Update Recursion for the Sum of Weighted Error Squares 571

13.5 Example:Single-Weight Adaptive Noise Canceler 572

13.6 Convergence Analysis of the RLS Algorithm 573

13.7 Computer Experiment on Adaptive Equalization 580

13.8 State-Space Formulation of the RLS Problem 583

Problems 587

13.9 Summary and Discussion 587

Chapter 14 Square-Root Adaptive Filters 589

14.1 Square-Root Kalman Filters 589

14.2 Building Square-Root Adaptive Filtering Algorithms on their Kalman FilterCounterparts 597

14.3 QR-RLS Algorithm 598

14.4 Extended QR-RLS Algorithm 614

14.5 Adaptive Beamforming 617

14.6 Inverse QR-RLS AIgorithm 624

14.7 Summary and Discussion 627

Problems 628

Chapter 15 Order-Recursive Adaptive Filters 630

15.1 Adaptive Forward Linear Prediction 631

15.2 Adaptive Backward Linear Prediction 634

15.3 Conversion Factor 636

15.4 Least-Squares Lattice Predictor 640

15.5 Angle-Normalized Estimation Errors 653

15.6 First-Order State-Space Models for Lattice Filtering 655

15.7 QR-Decomposition-Based Least-Squares Lattice Filters 660

15.8 Fundamental Properties of the QRD-LSL Filter 667

15.9 Computer Experiment on Adaptive Equalization 672

15.10 Extended QRD-LSL Algorithm 677

15 11 Recursive Least-Squares Lattice Filters Using A Posteriori Estimation Errors 679

15.12 Recursive LSL Filters Using A Priori Estimation Errors with Error Feedback 683

15.13 Computation of the Least-Squares Weight Vector 686

15.14 Computer Experiment on Adaptive Prediction 69l 693

15.15 Other Variants of Least-Squares Lattice Filters 693

15.16 Summary and Discussion 694

Problems 696

Chapter 16 Tracking of Time-Varying Systems 701

16.1 Markov Model for System Identification 702

16.2 Degree of Nonstationaritv 705

16.3 Criteria for Tracking Assessment 706

16.4 Tracking Performance of the LMS Algorithm 708

16.5 Tracking Performance of the RLS Algorithm 711

16.6 Comparison of the Tracking Performance of LMS and RLS Algorithms 716

16.7 Adaptive Recovery of a Chirped Sinusoid in Noise 719

16.8 How to Improve the Tracking Behavior of the RLS Algorithm 726

16.9 Computer Experiment on System Identification 729

16.10 Automatic Tuning ofAdaptation Constants 731

16.11 Summary and Discussion 736

Problems 737

Chapter 17 Finite-Precision Effects 738

17.1 Quantization Errors 739

17.2 Least-Mean-Square Algorithm 741

17.3 Recursive Least-Squares Algorithm 751

17.4 Square-Root Adaptive Filters 757

17.5 Order-Recursive Adaptive Filters 760

17.6 Fast Transversal Filters 763

17.7 Summary and Discussion 767

Problems 769

PART 4 NONLINEAR ADAPTIVE FILTERING 771

Chapter 18 Blind Deconvolution 772

18.1 Theoretical and Practical Considerations 773

18.2 Bussgang Algorithm for Blind Equalization of Real Baseband Channels 776

18.3 Extension of Bussgang Algorithms to Complex Baseband Channels 791

18.4 Special Cases of the Bussgang Algorithm 792

18.5 Blind Channel Identification and Equalization Using Polyspectra 796

18.6 Advantages and Disadvantages of HOS-Based Deconvolution Algorithms 802

18.7 Channel Identifiability Using Cyclostationary Statistics 803

18.8 Subspace Decomposition for Fractionally-Spaced Blind Identification 804

18.9 Summary and Discussion 813

Problems 814

Chapter 19 Back-Propagation Learning 817

19.1 Models of aNeuron 818

19.2 Multilayer Perceptron 822

19.3 Complex Back-Propagation Algorithm 824

19.4 Back-Propagation Algorithm for Real Parameters 837

19.5 Universal Approximation Theorem 838

19.6 Network Complexity 840

19.7 Filtering Applications 842

19.8 Summary and Discussion 852

Problems 854

Chapter 20 Radial Basis Function Networks 855

20.1 Structure of RBF Networks 856

20.2 Radial-Basis Functions 858

20.3 Fixed Centers Selected at Random 859

20.4 Recursive Hybrid Learning Procedure 862

20.5 Stochastic Gradient Approach 863

20.6 Universal Approximation Theorem(Revisited) 865

20.7 Filtering Applications 866

20.8 Summary and Discussion 871

Problems 873

Appendix A Complex Variables 875

Appendix B Differentiation with Respect to a Vector 890

Appendix C Method of Lagrange Multipliers 895

Appendix D Estimation Theory 899

Appendix E Maximum-Entropy Method 905

Appendix F Minimum-Variance Distortionless Response Spectrum 912

Appendix G Gradient Adaptive Lattice Algorithm 915

Appendix H Solution of the Difference Equation(9.75) 919

Appendix I Steady-State Analysis of the LMS Algorithm without Invoking the Inde-pendence Assumption 921

Appendix J The Complex Wishart Distribution 924

GIossary 928

Abbreviations 932

Principal Symbols 933

Bibliography 941

Index 978