CHAPTER 1 Introduction
1.1 Random Signals
1.2 Spectral Estimation
1.3 Signal Modeling
1.4 Adaptive Filtering
1.4.1 Applications of Adaptive Filters
1.4.2 Features of Adaptive Filters
1.5 Organization of the Book
CHAPTER 2 Random Sequences
2.1 Discrete-Time Stochastic Processes
2.1.1 Description Using Probability Functions
2.1.2 Second-Order Statistical Description
2.1.3 Stationarity
2.1.4 Ergodicity
2.1.5 Random Signal Variability
2.1.6 Frequency-Domain Description of Stationary Processes
2.2 Linear Systems with Stationary Random Inputs
2.2.1 Time-Domain Analysis
2.2.2 Frequency-Domain Analysis
2.2.3 Random Signal Memory
2.2.4 General Correlation Matrices
2.2.5 Correlation Matrices from Random Processes
2.3 Innovations Representation of Random Vectors
2.4 Principles of Estimation Theory
2.4.1 Properties of Estimators
2.4.2 Estimation of Mean
2.4.3 Estimation of Variance
2.5 Summary
Problems
CHAPTER 3 Linear Signal Models
3.1 Introduction
3.1.1 Linear Nonparametric Signal Models
3.1.2 Parametric Pole-Zero Signal Models
3.1.3 Mixed Processes and Wold Decomposition
3.2 All-Pole Models
3.2.1 Model Properties
3.2.2 All-Pole Modeling and Linear Prediction
3.2.3 Autoregressive Models
3.2.4 Lower-Order Models
3.3 All-Zero Models
3.3.1 Model Properties
3.3.2 Moving-Average Models
3.3.3 Lower-Order Models
3.4 Pole-Zero Models
3.4.1 Model Properties
3.4.2 Autoregressive Moving-Average Models
3.4.3 The First-Order Pole-Zero Model: PZ(1,1)
3.4.4 Summary and Dualities
3.5 Summary
Problems
CHAPTER 4 Nonparametric Power Spectrum Estimation
4.1 Spectral Analysis of Deterministic Signals
4.1.1 Effect of Signal Sampling
4.1.2 Windowing, Periodic Extension, and Extrapolation
4.1.3 Effect of Spectrum Sampling
4.1.4 Effects of Windowing: Leakage and Loss of Resolution
4.1.5 Summary
4.2 Estimation of the Autocorrelation of Stationary Random Signals
4.3 Estimation of the Power Spectrum of Stationary Random Signals
4.3.1 Power Spectrum Estimation Using the Periodogram
4.3.2 Power Spectrum Estimation by Smoothing a Single Periodogram--The Blackman-Tukey Method
4.3.3 Power Spectrum Estimation by Averaging Multiple Periodograms--The Welch-Bartlett Method
4.3.4 Some Practical Considerations and Examples
4.4 Multitaper Power Spectrum Estimation
4.5 Summary
Problems
CHAPTER 5 Optimum Linear Filters
5.1 Optimum Signal Estimation
5.2 Linear Mean Square Error Estimation
5.2.1 Error Performance Surface
5.2.2 Derivation of the Linear MMSE Estimator
5.2.3 Principal-Component Analysis of the Optimum Linear Estimator
5.2.4 Geometric Interpretations and the Principle of Orthogonality
5.2.5 Summary and Further Properties
5.3 Optimum Finite Impulse Response Filters
5.3.1 Design and Properties
5.3.2 Optimum FIR Filters for Stationary Processes
5.3.3 Frequency-Domain Interpretations
5.4 Linear Prediction
5.4.1 Linear Signal Estimation
5.4.2 Forward Linear Prediction
5.4.3 Backward Linear Prediction
5.4.4 Stationary Processes
5.4.5 Properties
5.5 Optimum Infinite Impulse Response Filters
5.5.1 Noncausal IIR Filters
5.5.2 Causal IIR Filters
5.5.3 Filtering of Additive Noise
5.5.4 Linear Prediction Using the Infinite Past--Whitening
5.6 Inverse Filtering and Deconvolution
5.7 Summary
Problems
CHAPTER 6 Algorthms and Structures for Optimum Linear Filters
6.1 Fundamentals of Order-Recursive Algorithms
6.1.1 Matrix Partitioning and Optimum Nesting .
6.1.2 Inversion of Partitioned Hermitian Matrices
6.1.3 Levinson Recursion for the Optimum Estimator
6.1.4 Order-Recursive Computation of the LDLH Decomposition
6.1.5 Order-Recursive Computation of the Optimum Estimate
6.2 Interpretations of Algorithmic Quantities
6.2.1 Innovations and Backward Prediction
6.2.2 Partial Correlation
6.2.3 Order Decomposition of the Optimum Estimate
6.2.4 Gram-Schmidt Orthogonalization
6.3 Order-Recursive Algorithms for Optimum FIR Filters
6.3.1 Order-Recursive Computation of the Optimum Filter
6.3.2 Lattice-Ladder Structure
6.3.3 Simplifications for Stationary Stochastic Processes
6.4 Algorithms of Levinson and Levinson-Durbin
6.5 Lattice Structures for Optimum Fir Filters And Predictors
6.5.1 Lattice-Ladder Structures
6.5.2 Some Properties and Interpretations
6.5.3 Parameter Conversions
6.6 Summary
Problems
CHAPTER 7 Least-Squares Filtering and Prediction
7.1 The Principle of Least Squares
7.2 Linear Least-Squares Error Estimation
7.2.1 Derivation of the Normal Equations
7.2.2 Statistical Properties of Least-Squares Estimaters
7.3 Least-Squares FIR Filters
7.4 Linear Least-Squares Signal Estimation
7.4.1 Signal Estimation and Linear Prediction
7.4.2 Combined Forward and Backward Linear Prediction(FBLP)
7.4.3 Narrowband Interference Cancelation
7.5 LS Computations Using the Normal Equations
7.5.1 Linear LSE Estimation
7.5.2 LSE FIR Filtering and Prediction
7.6 Summary
Problems
CHAPTER 8 Signal Modeling and Parametric Spectral Estimation
8.1 The Modeling Process: Theory and Practice
8.2 Estimation of All-Pole Models
8.2.1 Direct Structures
8.2.2 Lattice Structures
8.2.3 Maximum Entropy Method
8.2.4 Excitations with Line Spectra
8.3 Estimation Of Pole-Zero Models
8.3.1 Known Excitation
8.3.2 Unknown Excitation
8.4 Applications
8.4.1 Spectral Estimation
8.4.2 Speech Modeling
8.5 Harmonic Models and Frequency Estimation Techniques
8.5.1 Harmonic Model
8.5.2 Pisarenko Harmonic Decomposition
8.5.3 MUSIC Algorithm
8.5.4 Minimum-Norm Method
8.5.5 ESPRIT Algorithm
8.6 Summary
Problems
CHAPTER 9 Adaptive Filters
9.1 Typical Applications of Adaptive Filters
9.1.1 Echo Cancelation in Communications
9.1.2 Linear Predictive Coding
9.1.3 Noise Cancelation
9.2 Principles of Adaptive Filters
9.2.1 Features of Adaptive Filters
9.2.2 Optimum versus Adaptive Filters
9.2.3 Stability and Steady-State Performance of Adaptive Filters
9.2.4 Some Practical Considerations
9.3 Method of Steepest Descent
9.4 Least-Mean-Square Adaptive Filters
9.4.1 Derivation
9.4.2 Adaptation in a Stationary SOE
9.4.3 Summary and Design Guidelines
9.4.4 Applications of the LMS Algorithm
9.4.5 Some Practical Considerations
9.5 Recursive Least-Squares Adaptive Filters
9.5.1 LS Adaptive Filters
9.5.2 Conventional Recursive Least-Squares Algorithm
9.5.3 Some Practical Considerations
9.5.4 Convergence and Performance Analysis
9.6 Fast RLS Algorithms for FIR Filtering
9.6.1 Fast Fixed-Order RLS FIR Filters
9.6.2 RLS Lattice-Ladder Filters
9.6.3 RLS Lattice-Ladder Filters Using Error Feedback Updatings
9.7 Tracking Performance of Adaptive Algorithms
9.7.1 Approaches for Nonstationary SOE
9.7.2 Preliminaries in Performance Analysis
9.7.3 LMS Algorithm
9.7.4 RLS Algorithm with Exponential Forgetting
9.7.5 Comparison of Tracking Performance
9.8 Summary
Problems