1st Edition
Adaptive IIR Filtering in Signal Processing and Control
Integrates rational approximation with adaptive filtering, providing viable, numerically reliable procedures for creating adaptive infinite impulse response (IIR) filters. The choice of filter structure to adapt, algorithm design and the approximation properties for each type of algorithm are also addressed. This work recasts the theory of adaptive IIR filters by concentrating on recursive lattice filters, freeing systems from the need for direct-form filters.;A solutions manual is available for instructors only. College or university bookstores may order five or more copies at a special student price which is available upon request.
Preface
Introduction
Overview
Central Problem Statement
A Brief Glimpse into Approximation Criteria
Some Notations
Of Things not Belabored
Persistent Excitation
Parametrizations and Variances
Eruption Error versus Output Error
References
Recursive Filter Structures
Review of Linear System Theory
The Controllability and Observability Grammians
Minimality and Parametrization
Balanced Forms and Hankel Singular Value
Direct For Filters
Parallel and Cascade Forms
Tapped State Lattice Form
A Lattice Filter Primer
Schur Recursions
Bounded Real Lemma
Szegö Polynomials and Orthonormal Basis Functions
Relations with Direct Form Filter
Problems
References
The Beurling-Lax Theorem, Hankel Forms and Classical Identification
The Beurling-Lax Theorem
Shift-Invariant Subspaces
Orthogonal Filters and All-Pass Completions
Second Proof
Hankel Forms
Padé Approximations (Prony’s Method)
Equation Error Methods
Sufficient-Order Case
Undermodelled Case
Output Error Methods
Recapitulation
Problems
References
Rational Approximation in Hankel form
Problem Statement
Schmidt Form or SVD
The Hankel Norm
Nehari’s Theorem
Constructing the Hankel Norm Approximant
Repeated Hankel Singular Values
Some Bounds for Other Criteria
Problems
References
Rational H2 Approximation
Normality of the Rational H2 Approximation Problem
The Reduced Error Surface
Invariance to Frequency Transformations
Index of Stationary Points
Relations to the Hankel Norm Problem
Problems
References
Stability of Time-Varying Recursive Filters
Time-Varying Recursive Filters
BIBO and Exponential Stability
Slow Variation Analyses
Lyapunov Methods
Problems
References
Gradient Descent Algorithms
The Mean-Square Cost Function
Direct Form Algorithm
An Introduction to the ODE Method
Heuristics of the ODE Approach
Stability of Differential Equations
The Direct Approach of Lyapunov
The Indirect Method of Lyapunov
Lattice Gradient Descent Algorithm
Simplified Gradient Calculation
A Partial Gradient Algorithm
ODE for the Partial Gradient Algorithm
Algorithm Development
A Simplified Partial Gradient Algorithm
Alternate Formulate for the Rotation Angles
On Bounds for the Stepsize Constant μ
A Priori and A Posteriori Errors
The Ideal Update Formula
Linearization About a Minimum Point
Simulation Examples
Problems
References
The Steiglitz-McBride Family of Algorithms
The Steiglitz-McBride Methodology
Off-line Direct-Form Algorithm
Stationary Points of the Steiglitz-McBride Iteration
Influence of the Disturbance Term
Interpolation Constraints for the White Noise Input Case
Adaptive Filtering Algorithm: Direct Form
ODE for the Direct Form Algorithm
Convergence in the Sufficient-Order Case
A Lattice Version of the Steiglitz-McBride Iteration
Stationary Points of the Lattice Steiglit-McBride Iteration
Equivalence with Direct Form for General Inputs
Equivalence for White Noise Input Case
An A Priori Error Bound for White Noise Inputs
Eigenvalue Bound for Disturbance-Induced Term
Eigenvalue Bound for the Signal-Induced Term
On-Line Lattice Algorithm
Associated Differential Equation
Simulation Examples
Closing Remarks
Problems
References
Hyperstable Algorithms
Hyperstability Theorem
Positive Real Functions
Passive Impedance Functions
Spectral Factorization
Proof of Hyperstability Theorem
Hyperstability and Adaptive Filtering
A Simplified Hyperstable Algorithm
The Associated Differential Equation
A Lattice Version of SHARF
Relaxation of the SPR Condition
The Undermodelled Case
Stationary Points for General Inputs
White Noise Input Case
Problems
References
Adaptive Notch Filters
Introduction
Basic Principles
Notch Filter Approximations
Direct Form Notch Filter
Lattice Notch Filter
Gradient Descent Algorithms
A Simplified Lattice Algorithms
Pseudo Least-Squares Algorithms
Multiple Sinusoid Case
Gradient Descent Algorithms
Simplified Lattice Algorithm
Problems
References
Perspectives and Open Problems
Convergence in the Undermodelled Case
Szegö Polynomials
Spectrally Weighted L2 Criterion
Spectrally Weighted Balanced Systems
Weighted Hankel Forms
Hankel-Toeplitz Equations
Data-Driven Interpretation
Spectral Extensions of the Shift Operator
Spectrally Weighted Shift Operator
Prefiltered Signal Interpretation
References
Appendix A: Computations with Lattice Filters
Appendix B: List of Notations
Index
Biography
Phillip Regalia
". . .this is one of the better books in the field of system theory and signal processing. It is worth reading, and is definitely recommended. "
---International Journal of Electronics and Communications
