
Statistical and Adaptive Signal Processing
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Content
- Statistical and Adaptive Signal Processing
- Contents x
- Preface
- CHAPTER 1 Introduction 1
- 1.1 Random Signals 1
- 1.2 Spectral Estimation 8
- 1.3 Signal Modeling 11
- 1.4 Adaptive Filtering 16
- 1.5 Array Processing 25
- 1.6 Organization of the Book 29
- CHAPTER 2 Fundamentals of Discrete-Time Signal Processing 33
- 2.1 Discrete-Time Signals 33
- 2.2 Transform-Domian Represetation of Deterministic Signals 37
- 2.3 Discrete-Time Systems 47
- 2.4 Minimum Phase and System Invertibility 54
- 2.5 Lattice Filter Realizations 64
- 2.6 Summary 70
- Problems 70
- CHAPTER 3 Random Variables, Vectors, and Sequences 75
- 3.1 Random Variables 75
- 3.2 Random Vectors 83
- 3.3 Discrete-Time Stochastic Processes 97
- 3.4 Linear Systems with Stationary Random Inputs 115
- 3.5 Whitening and Innovations Representation 125
- 3.6 Principles of Estimation Theory 133
- 3.7 Summary 142
- Problems 143
- CHAPTER 4 Linear Signal Models 149
- 4.1 Introduction 149
- 4.2 All-Pole Models 156
- 4.3 All-Zero Models 172
- 4.5 Models with Poles on the Unit Circle 182
- 4.6 Cepstrum of Pole-Zero Models 184
- 4.7 Summary 189
- Problems 189
- CHAPTER 5 Nonparametric Power Spectrum Estimation 195
- 5.1 Spectral Analysis of Deterministic Signals 196
- 5.2 Estimation of the Autocorrelation of Stationary Random Signals 209
- 5.3 Estimation of the Power Spectrum of Stationary Random Signals 212
- 5.4 Joint Signal Analysis 237
- 5.5 Multitaper Power Spectrum Estimation 246
- 5.6 Summary 254
- Problems 255
- CHAPTER 6 Optimum Linear Filters 261
- 6.1 Optimum Signal Estimation 261
- 6.2 Linear Mean Square Error Estimation 264
- 6.3 Solution of the Normal Equations 274
- 6.4 Optimum Finite Impulse Response Filters 278
- 6.5 Linear Prediction 286
- 6.6 Optimum Infinite Impulse Response Filters 295
- 6.7 Inverse Filtering and Deconvolution 306
- 6.8 Channel Equalization in Data Transmission Systems 310
- 6.9 Matched Filters and Eigenfilters 319
- 6.10 Summary 325
- Problems 325
- CHAPTER 7 Algorithms and Structures for Optimum Linear Filters 333
- 7.1 Fundamentals of Order-Recursive Algorithms 334
- 7.2 Interpretations of Algorithmic Quantities 343
- 7.3 Order-Recursive Algorithms for Optiumum FIR Filters 347
- 7.4 Algorithms of Levinson and Levinson-Durbin 355
- 7.5 Lattice Structures for Optiumum FIR Filters and Predictors 361
- 7.6 Algorithm of Schur 368
- 7.7 Triangularization and Inversion of Toeplitz Matrices 374
- 7.8 Kalman Filter Algorithm 378
- 7.9 Summary 387
- Problems 389
- CHAPTER 8 Least-Squares Filtering and Prediction 395
- 8.1 The Principle of Least Squares 395
- 8.2 Linear Least-Squares Error Estimation 396
- 8.3 Least-Squares FIR Filters 406
- 8.4 Linear Least-Squares Signal Estimation 411
- 8.5 LS Computations Using the Normal Equations 416
- 8.6 LS Computations Using Orthogonalization Techniques 422
- 8.7 LS Computations Using the Signluar Value Decomposition 431
- 8.8 Summary 438
- Problems 439
- CHAPTER 9 Signal Modeling and Parametric Spectral Estimation 445
- 9.1 The Modeling Process: Theory and Practice 445
- 9.2 Estimation of All-Pole Models 449
- 9.3 Estimation of Pole-Zero Models 462
- 9.4 Applications 467
- 9.5 Minimum-Variance Specrum Estimation 471
- 9.6 Harmonic Models and Frequency Estimation Techniques 478
- 9.7 Summary 493
- Problems 494
- CHAPTER 10 Adaptive Filters 499
- 10.1 Typical Applications of Adaptive Fitlers 500
- 10.2 Principles of Adaptive Filters 506
- 10.4 Least-Mean-Square Adaptive Fitlers 524
- 10.5 Recursive Least-Squares Adaptive Filters 548
- 10.6 RLS Algorithms for Array Processing 560
- 10.7 Fast RLS Algorithms for FIR Filtering 573
- 10.8 Tracking Performance of Adaptive Algorithms 590
- 10.9 Summary 607
- Problems 608
- CHAPTER 11 Array Processing 621
- 11.1 Array Fundamentals 622
- 11.2 Conventional Spatial Filtering: Beamforming 631
- 11.3 Optiumum Array Processing 641
- 11.4 Performance Considerations for Optimum Beamformers 652
- 11.5 Adaptive Beamforming 659
- 11.6 Other Adaptive Array Processing Methods 671
- 11.7 Angle Estimation 678
- 11.8 Space-Time Adaptive Processing 683
- 11.9 Summary 685
- Problems 686
- CHAPTER 12 Further Topics 691
- 12.1 Higher-Order Statistics in Signal Processing 691
- 12.2 Blind Deconvolution 697
- 12.3 Unsupervised Adaptive Filters--Blind Equalizers
- 12.4 Fractionally Spaced Equalizers 709
- 12.5 Fractional Pole-Zero Signal Models 716
- 12.6 Self-Similar Random Signal Models 725
- 12.7 Summary 741
- Problems 742
- APPENDIX A Matrix Inversion Lemma 745
- APPENDIX B Gradients and Optimization in Complex Space 747
- B.1 Gradient 747
- B.2 LaGrange Multipliers 749
- APPENDIX C Matlab Functions 753
- APPENDIX D Useful Results from Matrix Algebra 755
- D.1 Complex-Valued Vector Space 755
- D.2 Matrices 756
- D.3 Determinant of a Square Matrix 760
- D.4 Unitary Matrices 762
- D.5 Positive Definite Matrices 764
- APPENDIX E Minimum Phase Test for Polynomials 767
- Bibliography 769
- Index 787
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