Statistical and Adaptive Signal Processing : Spectral Estimation, Signal Modeling, Adaptive Filtering and Array Processing

Preface xvii Introduction 1(32) Random Signals 1(7) Spectral Estimation 8(3) Signal Modeling 11(5) Rational or Pole-Zero Models Fractional Pole-Zero Models and Fractal Models Adaptive Filtering 16(9) Applications of Adaptive Filters Features of Adaptive Filters Array Processing 25(4) Spatial Filtering or Beamforming Adaptive Interference Mitigation in Radar Systems Adaptive Sidelobe Canceler Organization of the Book 29(4) Fundamentals of Discrete-Time Signal Processing 33(42) Discrete-Time Signals 33(4) Continuous-Time, Discrete-Time, and Digital Signals Mathematical Description of Signals Real-World Signals Transform-Domain Representation of Deterministic Signals 37(10) Fourier Transforms and Fourier Series Sampling of Continuous-Time Signals The Discrete Fourier Transform The z-Transform Representation of Narrowband Signals Discrete-Time Systems 47(7) Analysis of Linear, Time-Invariant Systems Response to Periodic Inputs Correlation Analysis and Spectral Density Minimum-Phase and System Invertibility 54(10) System Invertibility and Minimum-Phase Systems All-Pass Systems Minimum-Phase and All-Pass Decomposition Spectral Factorization Lattice Filter Realizations 64(6) All-Zero Lattice Structures All-Pole Lattice Structures Summary 70(5) Problems 70(5) Random Variables, Vectors, and Sequences 75(74) Random Variables 75(8) Distribution and Density Functions Statistical Averages Some Useful Random Variables Random Vectors 83(14) Definitions and Second-Order Moments Linear Transformations of Random Vectors Normal Random Vectors Sums of Independent Random Variables Discrete-Time Stochastic Processes 97(18) Description Using Probability Functions Second-Order Statistical Description Stationarity Ergodicity Random Signal Variability Frequency-Domain Description of Stationary Processes Linear Systems with Stationary Random Inputs 115(10) Time-Domain Analysis Frequency-Domain Analysis Random Signal Memory General Correlation Matrices Correlation Matrices from Random Processes Whitening and Innovations Representation 125(8) Transformations Using Eigen-decomposition Transformations Using Triangular Decomposition The Discrete Karhunen-Loeve Transform Principles of Estimation Theory 133(9) Properties of Estimators Estimation of Mean Estimation of Variance Summary 142(7) Problems 143(6) Linear Signal Models 149(46) Introduction 149(7) Linear Nonparametric Signal Models Parametric Pole-Zero Signal Models Mixed Processes and the Wold Decomposition All-Pole Models 156(16) Model Properties All-Pole Modeling and Linear Prediction Autoregressive Models Lower-Order Models All-Zero Models 172(5) Model Properties Moving-Average Models Lower-Order Models Pole-Zero Models 177(5) Model Properties Autoregressive Moving-Average Models The First-Order Pole-Zero Model 1: PZ (1,1) Summary and Dualities Models with Poles on the Unit Circle 182(2) Cepstrum of Pole-Zero Models 184(5) Pole-Zero Models All-Pole Models All-Zero Models Summary 189(6) Problems 189(6) Nonparametric Power Spectrum Estimation 195(66) Spectral Analysis of Deterministic Signals 196(13) Effect of Signal Sampling Windowing, Periodic Extension, and Extrapolation Effect of Spectrum Sampling Effects of Windowing: Leakage and Loss of Resolution Summary Estimation of the Autocorrelation of Stationary Random Signals 209(3) Estimation of the Power Spectrum of Stationary Random Signals 212(25) Power Spectrum Estimation Using the Periodogram Power Spectrum Estimation by Smoothing a Single Periodogram---The Blackman-Tukey Method Power Spectrum Estimation by Averaging Multiple Periodograms---The Welch-Bartlett Method Some Practical Considerations and Examples Joint Signal Analysis 237(9) Estimation of Cross-Power Spectrum Estimation of Frequency Response Functions Multitaper Power Spectrum Estimation 246(8) Estimation of Auto Power Spectrum Estimation of Cross Power Spectrum Summary 254(7) Problems 255(6) Optimum Linear Filters 261(72) Optimum Signal Estimation 261(3) Linear Mean Square Error Estimation 264(10) Error Performance Surface Derivation of the Linear MMSE Estimator Principal-Component Analysis of the Optimum Linear Estimator Geometric Interpretations and the Principle of Orthogonality Summary and Further Properties Solution of the Normal Equations 274(4) Optimum Finite Impulse Response Filters 278(8) Design and Properties Optimum FIR Filters for Stationary Processes Frequency-Domain Interpretations Linear Prediction 286(9) Linear Signal Estimation Forward Linear Prediction Backward Linear Prediction Stationary Processes Properties Optimum Infinite Impulse Response Filters 295(11) Noncausal IIR Filters Causal IIR Filters Filtering of Additive Noise Linear Prediction Using the Infinite Past---Whitening Inverse Filtering and Deconvolution 306(4) Channel Equalization in Data Transmission Systems 310(9) Nyquist's Criterion for Zero ISI Equivalent Discrete-Time Channel Model Linear Equalizers Zero-Forcing Equalizers Minimum MSE Equalizers Matched Filters and Eigenfilters 319(6) Deterministic Signal in Noise Random Signal in Noise Summary 325(8) Problems 325(8) Algorithms and Structures for Optimum Linear Filters 333(62) Fundamentals of Order-Recursive Algorithms 334(9) Matrix Partitioning and Optimum Nesting Inversion of Partitioned Hermitian Matrices Levinson Recursion for the Optimum Estimator Order-Recursive Computation of the LDLH Decomposition Order-Recursive Computation of the Optimum Estimate Interpretations of Algorithmic Quantities 343(4) Innovations and Backward Prediction Partial Correlation Order Decomposition of the Optimum Estimate Gram-Schmidt Orthogonalization Order-Recursive Algorithms for Optimum FIR Filters 347(8) Order-Recursive Computation of the Optimum Filter Lattice-Ladder Structure Simplifications for Stationary Stochastic Processes Algorithms Based on the UDUH Decomposition Algorithms of Levinson and Levinson-Durbin 355(6) Lattice Structures for Optimum FIR Filters and Predictors 361(7) Lattice-Ladder Structures Some Properties and Interpretations Parameter Conversions Algorithm of Schur 368(6) Direct Schur Algorithm Implementation Considerations Inverse Schur Algorithm Triangularization and Inversion of Toeplitz Matrices 374(4) LDLH Decomposition of Inverse of a Toeplitz Matrix LDLH Decomposition of a Toeplitz Matrix Inversion of Real Toeplitz Matrices Kalman Filter Algorithm 378(9) Preliminary Development Development of Kalman Filter Summary 387(8) Problems 389(6) Least-Squares Filtering and Prediction 395(50) The Principle of Least Squares 395(1) Linear Least-Squares Error Estimation 396(10) Derivation of the Normal Equations Statistical Properties of Least-Squares Estimators Least-Squares FIR Filters 406(5) Linear Least-Squares Signal Estimation 411(5) Signal Estimation and Linear Prediction Combined Forward and Backward Linear Prediction (FBLP) Narrowband Interference Cancelation LS Computations Using the Normal Equations 416(6) Linear LSE Estimation LSE FIR Filtering and Prediction LS Computations Using Orthogonalization Techniques 422(9) Householder Reflections The Givens Rotations Gram-Schmidt Orthogonalization LS Computations Using the Singular Value Decomposition 431(7) Singular Value Decomposition Solution of the LS Problem Rank-Deficient LS Problems Summary 438(7) Problems 439(6) Signal Modeling and Parametric Spectral Estimation 445(54) The Modeling Process: Theory and Practice 445(4) Estimation of All-Pole Models 449(13) Direct Structures Lattice Structures Maximum Entropy Method Excitations with Line Spectra Estimation of Pole-Zero Models 462(5) Known Excitation Unknown Excitation Nonlinear Least-Squares Optimization Applications 467(4) Spectral Estimation Speech Modeling Minimum-Variance Spectrum Estimation 471(7) Harmonic Models and Frequency Estimation Techniques 478(15) Harmonic Model Pisarenko Harmonic Decomposition Music Algorithm Minimum-Norm Method Esprit Algorithm Summary 493(6) Problems 494(5) Adaptive Filters 499(122) Typical Applications of Adaptive Filters 500(6) Echo Cancelation in Communications Equalization of Data Communications Channels Linear Predictive Coding Noise Cancelation Principles of Adaptive Filters 506(10) Features of Adaptive Filters Optimum versus Adaptive Filters Stability and Steady-State Performance of Adaptive Filters Some Practical Considerations Method of Steepest Descent 516(8) Least-Mean-Square Adaptive Filters 524(24) Derivation Adaptation in a Stationary SOE Summary and Design Guidelines Applications of the LMS Algorithm Some Practical Considerations Recursive Least-Squares Adaptive Filters 548(12) LS Adaptive Filters Conventional Recursive Least-Squares Algorithm Some Practical Considerations Convergence and Performance Analysis RLS Algorithms for Array Processing 560(13) LS Computations Using the Cholesky and QR Decompositions Two Useful Lemmas The QR-RLS Algorithm Extended QR-RLS Algorithm The Inverse QR-RLS Algorithm Implementation of QR-RLS Algorithm Using the Givens Rotations Implementation of Inverse QR-RLS Algorithm Using the Givens Rotations Classification of RLS Algorithms for Array Processing Fast RLS Algorithms for FIR Filtering 573(17) Fast Fixed-Order RLS FIR Filters RLS Lattice-Ladder Filters RLS Lattice-Ladder Filters Using Error Feedback Updatings Givens Rotation--Based LS Lattice-Ladder Algorithms Classification of RLS Algorithms for FIR Filtering Tracking Performance of Adaptive Algorithms 590(17) Approaches for Nonstationary SOE Preliminaries in Performance Analysis The LMS Algorithm The RLS Algorithm with Exponential Forgetting Comparison of Tracking Performance Summary 607(14) Problems 608(13) Array Processing 621(70) Array Fundamentals 622(9) Spatial Signals Modulation-Demodulation Array Signal Model The Sensor Array: Spatial Sampling Conventional Spatial Filtering: Beamforming 631(10) Spatial Matched Filter Tapered Beamforming Optimum Array Processing 641(11) Optimum Beamforming Eigenanalysis of the Optimum Beamformer Interference Cancelation Performance Tapered Optimum Beamforming The Generalized Sidelobe Canceler Performance Considerations for Optimum Beamformers 652(7) Effect of Signal Mismatch Effect of Bandwidth Adaptive Beamforming 659(12) Sample Matrix Inversion Diagonal Loading with the SMI Beamformer Implementation of the SMI Beamformer Sample-by-Sample Adaptive Methods Other Adaptive Array Processing Methods 671(7) Linearly Constrained Minimum-Variance Beamformers Partially Adaptive Arrays Sidelobe Cancelers Angle Estimation 678(5) Maximum-Likelihood Angle Estimation Cramer-Rao Lower Bound on Angle Accuracy Beamsplitting Algorithms Model-Based Methods Space-Time Adaptive Processing 683(2) Summary 685(6) Problems 686(5) Further Topics 691(54) Higher-Order Statistics in Signal Processing 691(6) Moments, Cumulants, and Polyspectra Higher-Order Moments and LTI Systems Higher-Order Moments of Linear Signal Models Blind Deconvolution 697(5) Unsupervised Adaptive Filters---Blind Equalizers 702(7) Blind Equalization Symbol Rate Blind Equalizers Constant-Modulus Algorithm Fractionally Spaced Equalizers 709(7) Zero-Forcing Fractionally Spaced Equalizers MMSE Fractionally Spaced Equalizers Blind Fractionally Spaced Equalizers Fractional Pole-Zero Signal Models 716(9) Fractional Unit-Pole Model Fractional Pole-Zero Models: FPZ (p, d, q) Symmetric α-Stable Fractional Pole-Zero Processes Self-Similar Random Signal Models 725(16) Self-Similar Stochastic Processes Fractional Brownian Motion Fractional Gaussian Noise Simulation of Fractional Brownian Motions and Fractional Gaussian Noises Estimation of Long Memory Fractional Levy Stable Motion Summary 741(4) Problems 742(3) Appendix A Matrix Inversion Lemma 745(2) Appendix B Gradients and Optimization in Complex Space 747(6) Gradient 747(2) Lagrange Multipliers 749(4) Appendix C Matlab Functions 753(2) Appendix D Useful Results from Matrix Algebra 755(12) Complex-Valued Vector Space 755(1) Some Definitions Matrices 756(4) Some Definitions Properties of Square Matrices Determinant of a Square Matrix 760(2) Properties of the Determinant Condition Number Unitary Matrices 762(2) Hermitian Forms after Unitary Transformations Significant Integral of Quadratic and Hermitian Forms Positive Definite Matrices 764(3) Appendix E Minimum Phase Test for Polynomials 767(2) Bibliography 769(18) Index 787