Statistical and Adaptive Signal Processing

, by Manolakis, Dimitris G.; Ingle, Vinay K.; Kogon, Stephen M.

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ISBN: 9781580536103 | 1580536107
Cover: Hardcover
Copyright: 4/30/2005

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This authoritative volume on statistical and adaptive signal processing offers you a unified, comprehensive and practical treatment of spectral estimation, signal modeling, adaptive filtering, and array processing. Packed with over 3,000 equations and more than 300 illustrations, this unique resource provides you with balanced coverage of implementation issues, applications, and theory, making it a smart choice for professional engineers and students alike.

Preface

xvii

Introduction

(32)

Random Signals

(7)

Spectral Estimation

(3)

Signal Modeling

(5)

Rational or Pole-Zero Models

Fractional Pole-Zero Models and Fractal Models

Adaptive Filtering

(9)

Applications of Adaptive Filters

Features of Adaptive Filters

Array Processing

(4)

Spatial Filtering or Beamforming

Adaptive Interference Mitigation in Radar Systems

Adaptive Sidelobe Canceler

Organization of the Book

(4)

Fundamentals of Discrete-Time Signal Processing

(42)

Discrete-Time Signals

(4)

Continuous-Time, Discrete-Time, and Digital Signals

Mathematical Description of Signals

Real-World Signals

Transform-Domain Representation of Deterministic Signals

(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

(7)

Analysis of Linear, Time-Invariant Systems

Response to Periodic Inputs

Correlation Analysis and Spectral Density

Minimum-Phase and System Invertibility

(10)

System Invertibility and Minimum-Phase Systems

All-Pass Systems

Minimum-Phase and All-Pass Decomposition

Spectral Factorization

Lattice Filter Realizations

(6)

All-Zero Lattice Structures

All-Pole Lattice Structures

Summary

(5)

Problems

(5)

Random Variables, Vectors, and Sequences

(74)

Random Variables

(8)

Distribution and Density Functions

Statistical Averages

Some Useful Random Variables

Random Vectors

(14)

Definitions and Second-Order Moments

Linear Transformations of Random Vectors

Normal Random Vectors

Sums of Independent Random Variables

Discrete-Time Stochastic Processes

(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

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Statistical and Adaptive Signal Processing

Summary

Author Biography

Table of Contents

Supplemental Materials