《自适应滤波器原理 英文版 第3版》求取 ⇩

Introduction1

1．The Filtering Problem1

2．Adaptive Filters2

3．Linear Filter Structures4

4．Approaches to the Development of Linear Adaptive Filtering Algorithms9

Contents13

Preface13

5．Real and Complex Forms of Adaptive Filters14

6．Nonlinear Adaptive Filters15

Acknowledgments16

7．Applications18

8．Some Historical Notes67

PART 1 BACKGROUND MATERIAL78

Chapter 1 Discrete-Time Signal Processing79

1.1 z-Transform79

1.2 Linear Time-Invariant Filters81

1.3 Minimum-Phase Filters86

1.4 Discrete Fourier Transform87

1.5 Implementing Convolutions Using the DFT87

1.6 Discrete Cosine Transform93

1.7 Summary and Discussion94

Problems95

Chapter 2 Stationary Processes and Models96

2.1 Partial Characterization of a Discrete-Time Stochastic Process97

2.2 Mean Ergodic Theorem98

2.3 Correlation Matrix100

2.4 Correlation Matrix of Sine Wave Plus Noi se106

2.5 Stochastic Models108

2.6 Wold Decomposition115

2.7 Asymptotic Stationarity of an Autoregressive Process116

2.8 Yule-Walker Equations118

2.9 Computer Experiment:Autoregressive Process of Order 2120

2.10 Selecting the Model Order128

2.11 Complex Gaussian Processes130

2.12 Summary and Discussion132

Problems133

Chapter 3 Spectrum Analysis136

3.1 Power Spectral Density136

3.2 Properties of Power Spectral Density138

3.3 Transmission of a Stationary Process Through a Linear Filter140

3.4 Cramér Spectral Representation for a Stationary Process144

3.5 Power Spectrum Estimation146

3.6 Other Statistical Characteristics of a Stochastic Process149

3.7 Polyspectra150

3.8 Spectral-Correlation Density154

3.9 Summary and Discussion157

Problems158

4.1 The Eigenvalue Problem160

Chapter 4 Eigenanalysis160

4.2 Properties of Eigenvalues and Eigenvectors162

4.3 Low-Rank Modeling176

4.4 Eigenfilters181

4.5 Eigenvalue Computations184

4.6 Summary and Discussion187

Problems188

PART 2 LINEAR OPTIMUM FILTERING193

Chapter 5 Wiener Filters194

5.1 Linear Optimum Filtering:Problem Statement194

5.2 Principle of Orthogonality197

5.3 Minimum Mean-Squared Error201

5.4 Wiener-Hopf Equations203

5.5 Error-Performance Surface206

5.6 Numerical Example210

5.7 Channel Equalization217

5.8 Linearly Constrained Minimum Variance Filter220

5.9 Generalized Sidelobe Cancelers227

5.10 Summary and Disussion235

Problems236

Chapter 6 Linear Prediction241

6.1 Forward Linear Prediction242

6.2 Backward Linear Prediction248

6.3 Levinson-Durbin Algorithm254

6.4 Properties of Prediction-Error Filters262

6.5 Schur-Cohn Test271

6.6 Autoregressive Modeling of a Stationary Stochastic Process273

6.7 Cholesky Factorization276

6.8 Lattice Predictors280

6.9 Joint-Process Estimation286

6.10 Block Estimation290

6.11 Summary and Discussion293

Problems295

Chapter 7 Kalman Filters302

7.1 Recursive Minimum Mean-Square Estimation for Scalar Random Variables303

7.2 Statement of the Kalman FiItering Problem306

7.3 The Innovations Process307

7.4 Estimation ofthe State using the Innovations Process310

7.5 Filtering317

7.6 Initial Conditions320

7.7 Summary of the Kalman FiIter320

7.8 Variants of the Kalman Filter322

7.9 The Extended Kalman Filter328

7.10 Summary and Discussion333

Problems334

PART 3 LINEAR ADAPTIVE FILTERING338

8.1 Some Preliminaries339

Chapter 8 Method of Steepest Descent339

8.2 Steepest-Descent Algorithm341

8.3 Stability of the Steepest-Descent Algorithm343

8.4 Example350

8.5 Summary and Discussion362

Problems362

Chapter 9 Least-Mean-Square Algorithm365

9.1 Overview of the Structure and Operation of the Least-Mean-Square Algorithm365

9.2 Least-Mean-Square Adaptation Algorithm367

9.3 Examples372

9.4 Stability and Performance Analysis of the LMS Algodthm390

9.5 Summary of the LMS Algorithm405

9.6 Computer Experiment on Adaptive Prediction406

9.7 Computer Experiment on Adaptive Equalization412

9.8 Computer Experiment on Minimum-Variance Distortionless Response Beamformer421

9.9 Directionality of Convergence of the LMS Algorithm for Non-White Inputs425

9.10 Robustness of the LMS Algorithm427

9.11 Normalized LMS Algorithm432

9.12 Summary and Discussion438

Problems439

Chapter 10 Frequency-Domain Adaptive Filters445

10.1 Block Adaptive Filters446

10.2 Fast LMS Algorithm451

10.3 Unconstrained Frequency-Domain Adaptive Filtering457

10.4 Self-Orthogonalizing Adaptive Filters458

10.5 Computer Experiment on Adaptive Equalization469

10.6 Classification ofAdaptive Filtering Algorithms477

10.7 Summary and Discussion478

Problems479

Chapter 11 Method of Least Squares483

11.1 Statement of the Linear Least-Squares Estimation Problem483

11.2 Data Windowing486

11.3 Principle of Orthogonality(Revisited)487

11.4 Minimum Sum ofError Squares491

11.5 Normal Equations and Linear Least-Squares Filters492

11.6 Time-Averaged Correlation Matrix495

11.7 Reformulation of the Normal Equations in Terms of Data Matrices497

11.8 Properties of Least-Squares Estimates502

11.9 Parametric Spectrum Estimation506

11.10 Singular Value Decomposition516

11.11 Pseudoinverse524

11.12 Interpretation of Singular Values and Singular Vectors525

11.13 Minimum Norm Solution to the Linear Least-Squares Problem526

11.14 Normalized LMS Algorithm Viewed as the Minimum-Norm Solution to anUnderdetermined Least-Squares Estimation Problem530

11.5 Summary and Discussion532

Problems533

Chapter 12 Rotations and Reflections536

12.1 Plane Rotations537

12.2 Two-Sided Jacobi Algorithm538

12.3 Cyclic Jacobi Algorithm544

12.4 Householder Transformation548

12.5 The QR Algorithm551

12.6 Summary and Discussion558

Problems560

Chapter 13 Recursive Least-Squares Algorithm562

13.1 Some Preliminaries563

13.2 The Matrix Inversion Lemma565

13.3 The Exponentially Weighted Recursive Least-Squares Algorithm566

13.4 Update Recursion for the Sum of Weighted Error Squares571

13.5 Example:Single-Weight Adaptive Noise Canceler572

13.6 Convergence Analysis of the RLS Algorithm573

13.7 Computer Experiment on Adaptive Equalization580

13.8 State-Space Formulation of the RLS Problem583

Problems587

13.9 Summary and Discussion587

Chapter 14 Square-Root Adaptive Filters589

14.1 Square-Root Kalman Filters589

14.2 Building Square-Root Adaptive Filtering Algorithms on their Kalman FilterCounterparts597

14.3 QR-RLS Algorithm598

14.4 Extended QR-RLS Algorithm614

14.5 Adaptive Beamforming617

14.6 Inverse QR-RLS AIgorithm624

14.7 Summary and Discussion627

Problems628

Chapter 15 Order-Recursive Adaptive Filters630

15.1 Adaptive Forward Linear Prediction631

15.2 Adaptive Backward Linear Prediction634

15.3 Conversion Factor636

15.4 Least-Squares Lattice Predictor640

15.5 Angle-Normalized Estimation Errors653

15.6 First-Order State-Space Models for Lattice Filtering655

15.7 QR-Decomposition-Based Least-Squares Lattice Filters660

15.8 Fundamental Properties of the QRD-LSL Filter667

15.9 Computer Experiment on Adaptive Equalization672

15.10 Extended QRD-LSL Algorithm677

15 11 Recursive Least-Squares Lattice Filters Using A Posteriori Estimation Errors679

15.12 Recursive LSL Filters Using A Priori Estimation Errors with Error Feedback683

15.13 Computation of the Least-Squares Weight Vector686

15.14 Computer Experiment on Adaptive Prediction 69l693

15.15 Other Variants of Least-Squares Lattice Filters693

15.16 Summary and Discussion694

Problems696

Chapter 16 Tracking of Time-Varying Systems701

16.1 Markov Model for System Identification702

16.2 Degree of Nonstationaritv705

16.3 Criteria for Tracking Assessment706

16.4 Tracking Performance of the LMS Algorithm708

16.5 Tracking Performance of the RLS Algorithm711

16.6 Comparison of the Tracking Performance of LMS and RLS Algorithms716

16.7 Adaptive Recovery of a Chirped Sinusoid in Noise719

16.8 How to Improve the Tracking Behavior of the RLS Algorithm726

16.9 Computer Experiment on System Identification729

16.10 Automatic Tuning ofAdaptation Constants731

16.11 Summary and Discussion736

Problems737

Chapter 17 Finite-Precision Effects738

17.1 Quantization Errors739

17.2 Least-Mean-Square Algorithm741

17.3 Recursive Least-Squares Algorithm751

17.4 Square-Root Adaptive Filters757

17.5 Order-Recursive Adaptive Filters760

17.6 Fast Transversal Filters763

17.7 Summary and Discussion767

Problems769

PART 4 NONLINEAR ADAPTIVE FILTERING771

Chapter 18 Blind Deconvolution772

18.1 Theoretical and Practical Considerations773

18.2 Bussgang Algorithm for Blind Equalization of Real Baseband Channels776

18.3 Extension of Bussgang Algorithms to Complex Baseband Channels791

18.4 Special Cases of the Bussgang Algorithm792

18.5 Blind Channel Identification and Equalization Using Polyspectra796

18.6 Advantages and Disadvantages of HOS-Based Deconvolution Algorithms802

18.7 Channel Identifiability Using Cyclostationary Statistics803

18.8 Subspace Decomposition for Fractionally-Spaced Blind Identification804

18.9 Summary and Discussion813

Problems814

Chapter 19 Back-Propagation Learning817

19.1 Models of aNeuron818

19.2 Multilayer Perceptron822

19.3 Complex Back-Propagation Algorithm824

19.4 Back-Propagation Algorithm for Real Parameters837

19.5 Universal Approximation Theorem838

19.6 Network Complexity840

19.7 Filtering Applications842

19.8 Summary and Discussion852

Problems854

Chapter 20 Radial Basis Function Networks855

20.1 Structure of RBF Networks856

20.2 Radial-Basis Functions858

20.3 Fixed Centers Selected at Random859

20.4 Recursive Hybrid Learning Procedure862

20.5 Stochastic Gradient Approach863

20.6 Universal Approximation Theorem(Revisited)865

20.7 Filtering Applications866

20.8 Summary and Discussion871

Problems873

Appendix A Complex Variables875

Appendix B Differentiation with Respect to a Vector890

Appendix C Method of Lagrange Multipliers895

Appendix D Estimation Theory899

Appendix E Maximum-Entropy Method905

Appendix F Minimum-Variance Distortionless Response Spectrum912

Appendix G Gradient Adaptive Lattice Algorithm915

Appendix H Solution of the Difference Equation(9.75)919

Appendix I Steady-State Analysis of the LMS Algorithm without Invoking the Inde-pendence Assumption921

Appendix J The Complex Wishart Distribution924

GIossary928

Abbreviations932

Principal Symbols933

Bibliography941

Index978