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More About This Title Adaptive Filters - Theory and Applications 2e
English
This second edition of Adaptive Filters: Theory and Applications has been updated throughout to reflect the latest developments in this field; notably an increased coverage given to the practical applications of the theory to illustrate the much broader range of adaptive filters applications developed in recent years. The book offers an easy to understand approach to the theory and application of adaptive filters by clearly illustrating how the theory explained in the early chapters of the book is modified for the various applications discussed in detail in later chapters. This integrated approach makes the book a valuable resource for graduate students; and the inclusion of more advanced applications including antenna arrays and wireless communications makes it a suitable technical reference for engineers, practitioners and researchers.
Key features:
• Offers a thorough treatment of the theory of adaptive signal processing; incorporating new material on transform domain, frequency domain, subband adaptive filters, acoustic echo cancellation and active noise control.
• Provides an in-depth study of applications which now includes extensive coverage of OFDM, MIMO and smart antennas.
• Contains exercises and computer simulation problems at the end of each chapter.
• Includes a new companion website hosting MATLAB® simulation programs which complement the theoretical analyses, enabling the reader to gain an in-depth understanding of the behaviours and properties of the various adaptive algorithms.
English
English
Preface xvii
Acknowledgments xxi
1 Introduction 1
1.1 Linear Filters 1
1.2 Adaptive Filters 2
1.3 Adaptive Filter Structures 3
1.4 Adaptation Approaches 7
1.5 Real and Complex Forms of Adaptive Filters 9
1.6 Applications 9
2 Discrete-Time Signals and Systems 28
2.1 Sequences and z-Transform 28
2.2 Parseval’s Relation 32
2.3 System Function 33
2.4 Stochastic Processes 35
Problems 44
3 Wiener Filters 48
3.1 Mean-Squared Error Criterion 48
3.2 Wiener Filter – Transversal, Real-Valued Case 50
3.3 Principle of Orthogonality 55
3.4 Normalized Performance Function 57
3.5 Extension to Complex-Valued Case 58
3.6 Unconstrained Wiener Filters 61
3.7 Summary and Discussion 79
Problems 80
4 Eigenanalysis and Performance Surface 90
4.1 Eigenvalues and Eigenvectors 90
4.2 Properties of Eigenvalues and Eigenvectors 91
4.3 Performance Surface 104
Problems 112
5 Search Methods 119
5.1 Method of Steepest Descent 120
5.2 Learning Curve 126
5.3 Effect of Eigenvalue Spread 130
5.4 Newton’s Method 131
5.5 An Alternative Interpretation of Newton’s Algorithm 133
Problems 135
6 LMS Algorithm 139
6.1 Derivation of LMS Algorithm 139
6.2 Average Tap-Weight Behavior of the LMS Algorithm 141
6.3 MSE Behavior of the LMS Algorithm 144
6.4 Computer Simulations 156
6.5 Simplified LMS Algorithms 167
6.6 Normalized LMS Algorithm 170
6.7 Affine Projection LMS Algorithm 173
6.8 Variable Step-Size LMS Algorithm 177
6.9 LMS Algorithm for Complex-Valued Signals 179
6.10 Beamforming (Revisited) 182
6.11 Linearly Constrained LMS Algorithm 186
Problems 190
Appendix 6A: Derivation of Eq. (6.39) 205
7 Transform Domain Adaptive Filters 207
7.1 Overview of Transform Domain Adaptive Filters 208
7.2 Band-Partitioning Property of Orthogonal Transforms 210
7.3 Orthogonalization Property of Orthogonal Transforms 211
7.4 Transform Domain LMS Algorithm 213
7.5 Ideal LMS-Newton Algorithm and Its Relationship with TDLMS 215
7.6 Selection of the Transform T 216
7.7 Transforms 229
7.8 Sliding Transforms 230
7.9 Summary and Discussion 242
Problems 243
8 Block Implementation of Adaptive Filters 251
8.1 Block LMS Algorithm 252
8.2 Mathematical Background 255
8.3 The FBLMS Algorithm 260
8.4 The Partitioned FBLMS Algorithm 267
8.5 Computer Simulations 276
Problems 279
Appendix 8A: Derivation of a Misadjustment Equation for the BLMS Algorithm 285
Appendix 8B: Derivation of Misadjustment Equations for the FBLMS Algorithms 288
9 Subband Adaptive Filters 294
9.1 DFT Filter Banks 295
9.2 Complementary Filter Banks 299
9.3 Subband Adaptive Filter Structures 303
9.4 Selection of Analysis and Synthesis Filters 304
9.5 Computational Complexity 307
9.6 Decimation Factor and Aliasing 308
9.7 Low-Delay Analysis and Synthesis Filter Banks 310
9.8 A Design Procedure for Subband Adaptive Filters 313
9.9 An Example 316
9.10 Comparison with FBLMS Algorithm 318
Problems 319
10 IIR Adaptive Filters 322
10.1 Output Error Method 323
10.2 Equation Error Method 327
10.3 Case Study I: IIR Adaptive Line Enhancement 332
10.4 Case Study II: Equalizer Design for Magnetic Recording Channels 343
10.5 Concluding Remarks 349
Problems 352
11 Lattice Filters 355
11.1 Forward Linear Prediction 355
11.2 Backward Linear Prediction 357
11.3 Relationship Between Forward and Backward Predictors 359
11.4 Prediction-Error Filters 359
11.5 Properties of Prediction Errors 360
11.6 Derivation of Lattice Structure 362
11.7 Lattice as an Orthogonalization Transform 367
11.8 Lattice Joint Process Estimator 369
11.9 System Functions 370
11.10 Conversions 370
11.11 All-Pole Lattice Structure 376
11.12 Pole-Zero Lattice Structure 376
11.13 Adaptive Lattice Filter 378
11.14 Autoregressive Modeling of Random Processes 383
11.15 Adaptive Algorithms Based on Autoregressive Modeling 385
Problems 400
Appendix 11A: Evaluation of E[ua(n)xT(n)K(n)x(n)uTa (n)] 407
Appendix 11B: Evaluation of the parameter γ 408
12 Method of Least-Squares 410
12.1 Formulation of Least-Squares Estimation for a Linear Combiner 411
12.2 Principle of Orthogonality 412
12.3 Projection Operator 415
12.4 Standard Recursive Least-Squares Algorithm 416
12.5 Convergence Behavior of the RLS Algorithm 421
Problems 430
13 Fast RLS Algorithms 433
13.1 Least-Squares Forward Prediction 434
13.2 Least-Squares Backward Prediction 435
13.3 Least-Squares Lattice 437
13.4 RLSL Algorithm 440
13.5 FTRLS Algorithm 453
Problems 460
14 Tracking 463
14.1 Formulation of the Tracking Problem 463
14.2 Generalized Formulation of LMS Algorithm 464
14.3 MSE Analysis of the Generalized LMS Algorithm 465
14.4 Optimum Step-Size Parameters 469
14.5 Comparisons of Conventional Algorithms 471
14.6 Comparisons Based on Optimum Step-Size Parameters 475
14.7 VSLMS: An Algorithm with Optimum Tracking Behavior 477
14.8 RLS Algorithm with Variable Forgetting Factor 485
14.9 Summary 486
Problems 488
15 Echo Cancellation 492
15.1 The Problem Statement 492
15.2 Structures and Adaptive Algorithms 495
15.3 Double-Talk Detection 512
15.4 Howling Suppression 521
15.5 Stereophonic Acoustic Echo Cancellation 524
Appendix 15A: Multitaper method 542
Appendix 15B: Derivation of the Two-Channel Levinson–Durbin
Algorithm 549
16 Active Noise Control 551
16.1 Broadband Feedforward Single-Channel ANC 553
16.2 Narrowband Feedforward Single-Channel ANC 559
16.3 Feedback Single-Channel ANC 573
16.4 Multichannel ANC Systems 577
Appendix 16A: Derivation of Eq. (16.46) 582
Appendix 16B: Derivation of Eq. (16.53) 583
17 Synchronization and Equalization in Data Transmission Systems 584
17.1 Continuous Time Channel Model 585
17.2 Discrete Time Channel Model and Equalizer Structures 589
17.3 Timing Recovery 593
17.4 Equalizers Design and Performance Analysis 606
17.5 Adaptation Algorithms 617
17.6 Cyclic Equalization 618
17.7 Joint Timing Recovery, Carrier Recovery, and Channel Equalization 628
17.8 Maximum Likelihood Detection 629
17.9 Soft Equalization 631
17.10 Single-Input Multiple-Output Equalization 643
17.11 Frequency Domain Equalization 645
17.12 Blind Equalization 649
Problems 654
18 Sensor Array Processing 659
18.1 Narrowband Sensor Arrays 660
18.2 Broadband Sensor Arrays 678
18.3 Robust Beamforming 683
Problems 692
19 Code Division Multiple Access Systems 695
19.1 CDMA Signal Model 695
19.2 Linear Detectors 699
19.3 Adaptation Methods 707
Problems 709
20 OFDM and MIMO Communications 711
20.1 OFDM Communication Systems 711
20.2 MIMO Communication Systems 730
20.3 MIMO–OFDM 743
Problems 743
References 746
Index 761
