Statistical Digital Signal Processing and

The main thrust is to provide students with a solid understanding of a number of important and related advanced topics in digital signal processing such as Wiener filters, power spectrum estimation, signal modeling and adaptive filtering. Scores of worked examples illustrate fine points, compare techniques and algorithms and facilitate comprehension of fundamental concepts. Also features an abundance of interesting and challenging problems at the end of every chapter.

Monson H. Hayes is the author of Statistical Digital Signal Processing and Modeling, published by Wiley.

Preface

xi

1 INTRODUCTION

1

(6)

2 BACKGROUND

7

(50)

2.1 Introduction

7

(1)

2.2 Discrete-Time Signal Processing

7

(13)

2.2.1 Discrete-Time Signals

8

(1)

2.2.2 Discrete-Time Systems

9

(3)

2.2.3 Time-Domain Descriptions of LSI Filters

12

(1)

2.2.4 The Discrete-Time Fourier Transform

12

(2)

2.2.5 The z-Transform

14

(2)

2.2.6 Special Classes of Filters

16

(2)

2.2.7 Filter Flowgraphs

18

(1)

2.2.8 The DFT and FFT

18

(2)

2.3 Linear Algebra

20

(32)

2.3.1 Vectors

21

(3)

2.3.2 Linear Independence, Vector Spaces, and Basis Vectors

24

(1)

2.3.3 Matrices

25

(2)

2.3.4 Matrix Inverse

27

(2)

2.3.5 The Determinant and the Trace

29

(1)

2.3.6 Linear Equations

30

(5)

2.3.7 Special Matrix Forms

35

(4)

2.3.8 Quadratic and Hermitian Forms

39

(1)

2.3.9 Eigenvalues and Eigenvectors

40

(8)

2.3.10 Optimization Theory

48

(4)

2.4 Summary

52

(1)

2.5 Problems

52

(5)

3 DISCRETE-TIME RANDOM PROCESSES

57

(72)

3.1 Introduction

57

(1)

3.2 Random Variables

58

(16)

3.2.1 Definitions

58

(4)

3.2.2 Ensemble Averages

62

(3)

3.2.3 Jointly Distributed Random Variables

65

(1)

3.2.4 Joint Moments

66

(1)

3.2.5 Independent, Uncorrelated and Orthogonal Random Variables

67

(1)

3.2.6 Linear Mean Square Estimation

68

(3)

3.2.7 Gaussian Random Variables

71

(1)

3.2.8 Parameter Estimation: Bias and Consistency

72

(2)

3.3 Random Processes

74

(25)

3.3.1 Definitions

74

(3)

3.3.2 Ensemble Averages

77

(4)

3.3.3 Gaussian Processes

81

(1)

3.3.4 Stationary Processes

81

(4)

3.3.5 The Autocovariance and Autocorrelation Matrices

85

(3)

3.3.6 Ergodicity

88

(5)

3.3.7 White Noise

93

(1)

3.3.8 The Power Spectrum

94

(5)

3.4 Filtering Random Processes

99

(5)

3.5 Spectral Factorization

104

(4)

3.6 Special Types of Random Processes

108

(10)

3.6.1 Autoregressive Moving Average Processes

108

(3)

3.6.2 Autoregressive Processes

111

(4)

3.6.3 Moving Average Processes

115

(1)

3.6.4 Harmonic Processes

116

(2)

3.7 Summary

118

(2)

3.8 Problems

120

(9)

4 SIGNAL MODELING

129

(86)

4.1 Introduction

129

(2)

4.2 The Least Squares (Direct) Method

131

(2)

4.3 The Pade Approximation

133

(11)

4.4 Prony's Method

144

(30)

4.4.1 Pole-Zero Modeling

144

(10)

4.4.2 Shanks' Method

154

(6)

4.4.3 All-Pole Modeling

160

(5)

4.4.4 Linear Prediction

165

(1)

4.4.5 Application: FIR Least Squares Inverse Filters

166

(8)

4.5 Iterative Prefiltering*

174

(3)

4.6 Finite Data Records

177

(11)

4.6.1 The Autocorrelation Method

178

(4)

4.6.2 The Covariance Method

182

(6)

4.7 Stochastic Models

188

(13)

4.7.1 Autoregressive Moving Average Models

189

(5)

4.7.2 Autoregressive Models

194

(1)

4.7.3 Moving Average Models

195

(3)

4.7.4 Application: Power Spectrum Estimation

198

(3)

4.8 Summary

201

(2)

4.9 Problems

203

(12)

5 THE LEVINSON RECURSION

215

(74)

5.1 Introduction

215

(1)

5.2 The Levinson-Durbin Recursion

216

(48)

5.2.1 Development of the Recursion

216

(7)

5.2.2 The Lattice Filter

223

(2)

5.2.3 Properties

225

(7)

5.2.4 The Step-Up and Step-Down Recursions

232

(6)

5.2.5 The Inverse Levinson-Durbin Recursion

238

(2)

5.2.6 The Schur Recursion*

240

(10)

5.2.7 The Cholesky Decomposition

250

(4)

5.2.8 The Autocorrelation Extension Problem

254

(2)

5.2.9 Inverting a Toeplitz Matrix

256

(8)

5.3 The Levinson Recursion

264

(4)

5.4 The Split Levinson Recursion*

268

(8)

5.5 Summary

276

(3)

5.6 Problems

279

(10)

6 LATTICE FILTERS

289

(46)

6.1 Introduction

289

(1)

6.2 The FIR Lattice Filter

289

(5)

6.3 Split Lattice Filter

294

(3)

6.4 IIR Lattice Filters

297

(10)

6.4.1 All-pole Filter

297

(2)

6.4.2 Other All-pole Lattice Structures

299

(5)

6.4.3 Lattice Filters Having Poles and Zeros

304

(3)

6.5 Lattice Methods for All-Pole Signal Modeling

307

(18)

6.5.1 The Forward Covariance Method

308

(5)

6.5.2 The Backward Covariance Method

313

(2)

6.5.3 Variations

315

(1)

6.5.4 Burg's Method

316

(6)

6.5.5 Modified Covariance Method

322

(3)

6.6 Stochastic Modeling

325

(2)

6.7 Summary

327

(2)

6.8 Problems

329

(6)

7 WIENER FILTERING

335

(56)

7.1 Introduction

335

(2)

7.2 The FIR Wiener Filter

337

(16)

7.2.1 Filtering

339

(3)

7.2.2 Linear Prediction

342

(7)

7.2.3 Noise Cancellation

349

(3)

7.2.4 Lattice Representation for the FIR Wiener Filter

352

(1)

7.3 The IIR Wiener Filter

353

(18)

7.3.1 Noncausal IIR Wiener Filter

353

(5)

7.3.2 The Causal IIR Wiener Filter

358

(3)

7.3.3 Causal Wiener Filtering

361

(4)

7.3.4 Causal Linear Prediction

365

(4)

7.3.5 Wiener Deconvolution

369

(2)

7.4 Discrete Kalman Filter

371

(8)

7.5 Summary

379

(1)

7.6 Problems

380

(11)

8 SPECTRUM ESTIMATION

391

(102)

8.1 Introduction

391

(2)

8.2 Nonparametric Methods

393

(33)

8.2.1 The Periodogram

393

(5)

8.2.2 Performance of the Periodogram

398

(10)

8.2.3 The Modified Periodogram

408

(4)

8.2.4 Bartlett's Method: Periodogram Averaging

412

(3)

8.2.5 Welch's Method: Averaging Modified Periodograms

415

(5)

8.2.6 Blackman-Tukey Approach: Periodogram Smoothing

420

(4)

8.2.7 Performance Comparisons

424

(2)

8.3 Minimum Variance Spectrum Estimation

426

(7)

8.4 The Maximum Entropy Method

433

(7)

8.5 Parametric Methods

440

(11)

8.5.1 Autoregressive Spectrum Estimation

441

(7)

8.5.2 Moving Average Spectrum Estimation

448

(1)

8.5.3 Autoregressive Moving Average Spectrum Estimation

449

(2)

8.6 Frequency Estimation

451

(18)

8.6.1 Eigendecomposition of the Autocorrelation Matrix

451

(8)

8.6.2 Pisarenko Harmonic Decomposition

459

(4)

8.6.3 MUSIC

463

(2)

8.6.4 Other Eigenvector Methods

465

(4)

8.7 Principal Components Spectrum Estimation

469

(4)

8.7.1 Bartlett Frequency Estimation

470

(1)

8.7.2 Minimum Variance Frequency Estimation

471

(1)

8.7.3 Autoregressive Frequency Estimation

472

(1)

8.8 Summary

473

(4)

8.9 Problems

477

(16)

9 ADAPTIVE FILTERING

493

(78)

9.1 Introduction

493

(4)

9.2 FIR Adaptive Filters

497

(37)

9.2.1 The Steepest Descent Adaptive Filter

499

(6)

9.2.2 The LMS Algorithm

505

(1)

9.2.3 Convergence of the LMS Algorithm

506

(8)

9.2.4 Normalized LMS

514

(2)

9.2.5 Application: Noise Cancellation

516

(5)

9.2.6 Other LMS-Based Adaptive Filters

521

(5)

9.2.7 Gradient Adaptive Lattice Filter

526

(2)

9.2.8 Joint Process Estimator

528

(2)

9.2.9 Application: Channel Equalization

530

(4)

9.3 Adaptive Recursive Filters

534

(7)

9.4 Recursive Least Squares

541

(13)

9.4.1 Exponentially Weighted RLS

541

(7)

9.4.2 Sliding Window RLS

548

(3)

9.4.3 Summary

551

(3)

9.5 Problems

554

(17)

Appendix USE OF MATLAB PROGRAMS

571

(24)

A.1 Introduction

571

(1)

A.2 General Information

572

(2)

A.3 Random Processes

574

(1)

A.4 Signal Modeling

574

(4)

A.5 Levinson Recursion

578

(4)

A.6 Lattice Filters

582

(1)

A.7 Optimum Filters

583

(1)

A.8 Spectrum Estimation

584

(8)

A.9 Adaptive Filtering

592

(3)

Table of Symbols

595

(4)

Index

599

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Statistical Digital Signal Processing and Modeling

Summary

Author Biography

Table of Contents

Supplemental Materials