Polynomial signal processing /

Polynomial signal processing /

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Bibliographic Details
Author / Creator:Mathews, V. John.
Imprint:New York : Wiley, c2000.
Description:xvii, 452 p. : ill. ; 24 cm.
Language:English
Subject:
Signal processing.
Nonlinear theories.
Filters (Mathematics)
Filters (Mathematics)
Nonlinear theories.
Signal processing.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/5630683
Hidden Bibliographic Details
Other authors / contributors:Sicuranza, Giovanni L.
ISBN:0471034142 (alk. paper)
Notes:"A Wiley-Interscience publication."
Includes bibliographical references and index.
Table of Contents:
  • Preface
  • 1. Introduction
  • 1.1. Examples in Applications of Nonlinear Filters
  • 1.1.1. Communication Systems
  • 1.1.2. Perceptually Tuned Signal Processing
  • 1.1.3. Harmonic Distortion in Loudspeakers
  • 1.1.4. Enhancement of Noisy Images
  • 1.1.5. Motion of Moored Ships in Ocean Waves
  • 1.1.6. Distortions in Magnetic Recording Systems
  • 1.2. Classes of Nonlinear Systems
  • 1.2.1. Homomorphic Systems
  • 1.2.2. Order Statistic Filters
  • 1.2.3. Morphological Filters
  • 1.2.4. Neural Networks
  • 1.2.5. Polynomial Filters
  • 1.3. Organization of the Book
  • 1.4. A Brief History of Polynomial Signal Processing
  • 1.4.1. Volterra's Work
  • 1.4.2. Wiener and His Influence
  • 1.4.3. Early Work on Discrete-Time Systems
  • 1.4.4. Adaptive Polynomial Filters
  • 1.4.5. Frequency-Domain Methods
  • 1.4.6. Recursive Polynomial Systems
  • 1.4.7. Some Early Applications
  • 2. Volterra Series Expansions
  • 2.1. Continuous-Time Systems
  • 2.1.1. Linear Shift-Invariant Systems
  • 2.1.2. Volterra Series Expansion for Nonlinear Systems
  • 2.1.3. Limitations of Volterra Series Expansions
  • 2.2. Discrete-Time Systems
  • 2.2.1. DTI Nonlinear Systems
  • 2.3. Properties of Volterra Series Expansions
  • 2.3.1. Linearity with Respect to the Kernel Coefficients
  • 2.3.2. Multidimensional Convolution Property
  • 2.3.3. Stability
  • 2.3.4. Symmetry of the Kernels and Equivalent Representations
  • 2.3.5. Kernel Complexity
  • 2.3.6. Impulse Responses of Polynomial Filters
  • 2.4. Existence and Convergence of Volterra Series Expansions
  • 2.4.1. Special Classes of Polynomial Systems
  • 2.5. Transform-Domain Representations of Volterra Systems
  • 2.5.1. Response to a Complex Sinusoid
  • 2.5.2. Response to Multiple Complex Sinusoids
  • 2.5.3. Response to a Signal with a Continuous Spectrum
  • 2.5.4. The z-Transform Representation
  • 2.5.5. The Discrete Fourier Transform Representation
  • 2.5.6. Symmetry of H[subscript p](k[subscript 1], k[subscript 2],..., k[subscript p])
  • 2.6. Exercises
  • 3. Realization of Truncated Volterra Filters
  • 3.1. Algebraic Representation of Quadratic Filters
  • 3.1.1. Matrix-Vector Representation
  • 3.1.2. Vector Representation
  • 3.2. Realization of Quadratic Filters
  • 3.2.1. Direct-Form Realization
  • 3.2.2. Realization Based on the Convolution Property
  • 3.2.3. Structures Based on Matrix Decompositions
  • 3.2.4. Structures Based on Distributed Arithmetic
  • 3.2.5. FFT-Based Realization of Quadratic Filters
  • 3.3. Constraints Imposed on Quadratic Filters
  • 3.3.1. Isotropy
  • 3.3.2. Preservation of a Constant Input Value
  • 3.3.3. Preservation of Bias
  • 3.3.4. Spectral Constraints
  • 3.4. Realization of Higher-Order Volterra Filters
  • 3.4.1. Parallel-Cascade Realization of Higher-Order Volterra Filters
  • 3.4.2. Distributed Arithmetic Realizations of Higher-Order Operators
  • 3.4.3. FFT-Based Realization of Higher-Order Volterra Filters
  • 3.5. Exercises
  • 4. Multidimensional Volterra Filters
  • 4.1. Multidimensional Volterra Series Expansion
  • 4.1.1. Vector Representation of Linear Multidimensional Filters with Finite Memory
  • 4.1.2. Vector Representation of Finite-Support Multidimensional Volterra Filters
  • 4.2. Realizations of Multidimensional Volterra Filters
  • 4.2.1. Direct-Form Realization
  • 4.2.2. Realization of Quadratic Filters through Matrix Decomposition
  • 4.2.3. Realization of Multidimensional Volterra Filters Using Distributed Arithmetic
  • 4.3. Constraints Imposed on Two-Dimensional Quadratic Filters
  • 4.3.1. Isotropy of Two-Dimensional Quadratic Systems
  • 4.3.2. Typical Gray-Scale Constraints Imposed on Two-Dimensional Filters in Image Processing Applications
  • 4.4. Design of Two-Dimensional Quadratic Filters
  • 4.4.1. Optimization Methods for Quadratic Filter Design
  • 4.4.2. Design Using the Bi-Impulse Response Signals
  • 4.5. Exercises
  • 5. Parameter Estimation
  • 5.1. The Truncated Volterra Series Estimation Problem
  • 5.1.1. Optimality of the Volterra Series Models
  • 5.1.2. Sampling Requirements for Volterra System Identification
  • 5.2. Direct Estimation of the Parameters
  • 5.2.1. The MMSE Formulation
  • 5.2.2. Least-Squares Formulation
  • 5.2.3. Condition for Invertibility of the Autocorrelation Matrix
  • 5.3. Orthogonal Methods for System Identification
  • 5.3.1. Basic Definitions and Motivation
  • 5.3.2. Wiener G-Functionals
  • 5.3.3. Structure of the G-Functionals
  • 5.3.4. System Identification Using G-Functionals
  • 5.3.5. Orthogonalization of Correlated Gaussian Signals
  • 5.4. Lattice Orthogonalization for Arbitrary Input Signals
  • 5.4.1. Multichannel Representation of Nonlinear Systems
  • 5.4.2. The Nonlinear Lattice Prediction
  • 5.4.3. Joint Process Estimation Using the Orthogonal Basis Signal Set
  • 5.5. Identification of Cascade Nonlinear Systems
  • 5.6. Exercises
  • 6. Frequency-Domain Methods for Volterra System Identification
  • 6.1. Higher-Order Statistics
  • 6.1.1. Cumulants of Gaussian Random Variables
  • 6.1.2. Relationship between Cumulants and Moments
  • 6.1.3. Additional Properties of Cumulants
  • 6.1.4. Higher-Order Statistics of Discrete-Time Stationary Processes
  • 6.1.5. Cumulant Spectra
  • 6.2. Identification of Truncated Volterra Systems Using Cumulant Spectra
  • 6.2.1. A Useful Result
  • 6.2.2. Identification of Homogeneous Volterra Systems
  • 6.2.3. Identification of Quadratic Systems
  • 6.2.4. Identification of the Kernels of a pth-Order Volterra System
  • 6.3. Estimation of Quadratic Systems Using Arbitrary Input Signals
  • 6.3.1. The System Model
  • 6.3.2. The Parameter Estimation Algorithm
  • 6.3.3. Computational Issues
  • 6.3.4. Extension to Higher-Order Volterra Systems
  • 6.4. Exercises
  • 7. Adaptive Truncated Volterra Filters
  • 7.1. Adaptive Filters Using Linear Models
  • 7.1.1. Stochastic Gradient Adaptive Filters
  • 7.1.2. Least-Mean-Square Adaptive Filters
  • 7.1.3. Recursive Least-Squares Adaptive Filters
  • 7.2. Stochastic Gradient Truncated Volterra Filters
  • 7.2.1. The Least-Mean-Square Adaptive Second-Order Volterra Filter
  • 7.3. RLS Adaptive Volterra Filters
  • 7.3.1. Stability of RLS Adaptive Filters
  • 7.3.2. Performance Evaluation of RLS Adaptive Volterra Filters
  • 7.3.3. Approximate RLS Volterra Filters
  • 7.4. Fast RLS Truncated Volterra Filters
  • 7.4.1. The Basic Approach to Computational Simplifications
  • 7.4.2. Strategy for Updating the Gain Vector
  • 7.4.3. Solving for the Augmented Gain Vector
  • 7.4.4. Another Expression for the Augmented Gain Vector
  • 7.4.5. Update for the Gain Vector
  • 7.4.6. The Final Pieces of the Derivation
  • 7.4.7. The Complete Algorithm
  • 7.4.8. Extension to Higher-Order Volterra Filters
  • 7.4.9. Numerical Properties of the Fast RLS Volterra Filter
  • 7.5. Adaptive Volterra Filters Using Distributed Arithmetic
  • 7.5.1. A Simpler Update Equation
  • 7.6. Adaptive Lattice Volterra Filters for Gaussian Inputs
  • 7.6.1. An Adaptive Lattice Linear Predictor
  • 7.6.2. Extending the Adaptive Lattice Predictor to the Second-Order Volterra Filtering
  • 7.7. Adaptive Filters for Parallel-Cascade Structures
  • 7.7.1. LMS Adaptation for the Parallel-Cascade Structure
  • 7.8. Block Adaptive LMS Volterra Filters
  • 7.8.1. Time-Domain Block Adaptation
  • 7.8.2. Frequency-Domain Adaptive LMS Volterra Filter
  • 7.8.3. Computational Complexity
  • 7.9. Exercises
  • 8. Recursive Polynomial Systems
  • 8.1. Volterra Series Expansion for Bilinear Systems
  • 8.2. Stability of Bilinear Systems
  • 8.2.1. Comments on the Stability Theorem
  • 8.3. Adaptive Bilinear Filters
  • 8.3.1. Equation Error Adaptive Bilinear Filters
  • 8.3.2. Output Error Bilinear Filters
  • 8.3.3. LMS Adaptive Output Error Bilinear Filters
  • 8.3.4. Additional Work on Adaptive Recursive Polynomial Filters
  • 8.4. A Performance Comparison of Three System Models in an Equalization Problem
  • 8.5. Exercises
  • 9. Inversion and Time Series Analysis
  • 9.1. Inversion of Nonlinear Systems
  • 9.1.1. Exact Inverses
  • 9.1.2. pth-Order Inverses
  • 9.2. Polynomial Time Series Analysis
  • 9.2.1. A Specific Bilinear Model
  • 9.3. Exercises
  • 10. Applications of Polynomial Filters
  • 10.1. Choice of System Models
  • 10.2. Compensation of Nonlinear Distortions
  • 10.2.1. Techniques for Linearization
  • 10.2.2. Linearization of Loudspeaker Nonlinearities
  • 10.3. Applications in Communication Systems
  • 10.3.1. Nonlinear Echo Cancellation
  • 10.3.2. Equalization of Communication Channels
  • 10.3.3. Predistortion for Nonlinear Channels
  • 10.4. The Frequency and Amplitude Estimation
  • 10.5. Speech Modeling
  • 10.6. Polynomial Filters for Image Processing
  • 10.6.1. Edge Extraction
  • 10.6.2. Image Enhancement
  • 10.6.3. Processing of Document Images
  • 10.7. Polynomial Processing of Image Sequences
  • 10.7.1. Prediction of Image Sequences
  • 10.7.2. Interpolation of Image Sequences
  • 10.8. A Brief Overview of Some More Applications
  • 10.8.1. Adaptive Noise Cancellation
  • 10.8.2. Stabilization of Moored Vessels in Random Sea Waves
  • 10.8.3. Signal Detection
  • 10.9. Exercises
  • 11. Some Related Topics and Recent Developments
  • 11.1. Nonlinear Classifiers
  • 11.1.1. Higher-Order Neural Networks
  • 11.1.2. Polynomial Invariants
  • 11.2. Evaluation of Local Intrinsic Dimensionality
  • 11.3. Rational Filters
  • 11.3.1. Estimation of the Parameters of a Rational Filter
  • 11.3.2. Rational Filters for Image Processing
  • 11.4. Blind Identification and Equalization of Nonlinear Channels
  • 11.5. New Mathematical Formulations
  • 11.5.1. A Diagonal Coordinate Representation for Volterra Filters
  • 11.5.2. V-Vector Algebra for Adaptive Volterra Filters
  • 11.6. An Application of Volterra Filters in Computer Engineering
  • Appendix A. Properties of Kronecker Products
  • Appendix B. LU Decomposition of Square Matrices
  • Appendix C. Linear Lattice Predictors
  • References
  • Index
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