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E-raamat: Adaptive IIR Filtering in Signal Processing and Control

(Institut National des Telecommunications, Evry Cedex, France)
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For graduate students, their professors, and research scientists, this reference-text integrates rational approximation with adaptive filtering, providing viable, numerically reliable procedures for creating adaptive infinite impulse response (IIR) filters and addressing the choice of filter structure to adapt. It recasts the theory of adaptive IIR filters by concentrating on recursive lattice filters, freeing systems from the need for direct-form filters. Annotation copyright Book News, Inc. Portland, Or.

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.

Arvustused

". . .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

Preface v
Introduction
1(30)
Overview
1(4)
Central Problem Statement
5(7)
A Brief Glimpse into Approximation Criteria
12(2)
Some Notations
14(5)
Of Things not Belabored
19(12)
Persistent Excitation
19(4)
Parametrizations and Variances
23(4)
Equation Error versus Output Error
27(2)
References
29(2)
Recursive Filter Structures
31(51)
Review of Linear System Theory
31(6)
Controllability and observability Grammians
32(2)
Minimality and parametrization
34(1)
Balanced Forms and hankel Singular Values
35(2)
Direct Form Filters
37(4)
Parallel and Cascade Forms
41(2)
Tapped State Lattice Form
43(39)
A Lattice Filter Primer
48(7)
Schur Recursions
55(2)
Bounded Real Lemma
57(1)
Szego Polynomials and Orthonormal Basis Functions
58(4)
Relations with Direct Form Filter
62(2)
Problems
64(14)
References
78(4)
The Beurling-Lax Theorem, Hankel Forms, and Classical Identification
82(63)
The Beurling-Lax Theorem
83(14)
Shift-Invariant Subspaces
84(3)
Orthogonal Filters and All-Pass Completions
87(8)
Second Proof
95(2)
Hankel Forms
97(5)
Pade Approximations (Prony's Method)
102(8)
Equation Error Methods
110(11)
Sufficient-Order Case
112(3)
Undermodelled Case
115(6)
Output Error Methods
121(10)
Recapitulation
131(14)
Problems
133(9)
References
142(3)
Rational Approximation in Hankel Norm
145(35)
Problem Statement
146(1)
Schmidt Form or SVD
147(3)
The Hankel Norm
150(4)
Nehari's Theorem
154(5)
Constructing the Hankel Norm Approximant
159(6)
Repeated hankel Singular Values
165(3)
Some Bounds for Other Criteria
168(12)
Problems
169(9)
References
178(2)
Rational H2 Approximation
180(48)
Normality of the Rational H2 Approximation Problem
182(5)
The Reduced Error Surface
187(11)
Invariance to Frequency Transformations
198(7)
Index of Stationary Points
205(3)
Relations to the Hankel Norm Problem
208(20)
Problems
215(11)
References
226(2)
Stability of Time-Varying Recursive Filters
228(30)
Time-Varying Recursive Filters
228(6)
BIBO and Exponential Stability
234(4)
Slow Variation Analyses
238(4)
Lyapunov Methods
242(16)
Problems
249(8)
References
257(1)
Gradient Descent Algorithms
258(116)
The Mean-Square Cost Function
260(7)
Direct Form Algorithm
267(6)
An Introduction to the ODE Method
273(10)
Heuristics of the ODE Approach
275(3)
Stability of Differential Equations
278(1)
The Direct Approach of Lyapunov
279(2)
The Indirect Method of Lyapunov
281(2)
Lattice Gradient Descent Algorithm
283(7)
Simplified Gradient Calculation
290(16)
A Partial Gradient Algorithm
306(18)
ODE for the Partial Gradient Algorithm
313(4)
Algorithm Development
317(7)
A Simplified Partial Gradient Algorithm
324(10)
Alternate Formulae for the Rotation Angles
334(10)
On Bounds for the Stepsize Constant μ
344(7)
A Priori and A Posteriori Errors
345(3)
The ideal Update Formula
348(1)
Linearization About a Minimum Point
349(2)
Simulation Examples
351(23)
Problems
363(8)
References
371(3)
The Steiglitz-McBride Family of Algorithms
374(113)
The Steiglitz-McBride Methodology
376(2)
Off-Line Direct-Form Algorithm
378(8)
Stationary Points of the Steiglitz-McBride Iteration
386(11)
Influence of the Disturbance Term
397(5)
Interpolation Constraints for the White Noise Input Case
402(3)
Adaptive Filtering Algorithm: Direct Form
405(13)
ODE for the Direct Form Algorithm
410(2)
Convergence in the Sufficient-Order Case
412(6)
A Lattice Version of the Steiglitz-McBride Iteration
418(7)
Stationary Points of the Lattice Steiglit-McBride Iteration
425(17)
Equivalence with Direct Form for General Inputs
433(3)
Equivalence for White Noise Input Case
436(6)
An A Priori Error Bound for White Noise Inputs
442(12)
Eigenvalue Bound for Disturbance-Induced Term
447(2)
Eigenvalue Bound for the Signal-Induced Term
449(5)
On-Line Lattice Algorithm
454(13)
Associated Differential Equation
460(7)
Simulation Examples
467(2)
Closing Remarks
469(18)
Problems
473(11)
References
484(3)
Hyperstable Algorithms
487(67)
Hyperstability Theorem
489(11)
Positive Real Functions
490(3)
Passive Impedance Functions
493(2)
Spectral Factorization
495(2)
Proof of Hyperstability Theorem
497(3)
Hyperstability and Adaptive Filtering
500(7)
A Simplified Hyperstable Algorithm
507(3)
The Associated Differential Equation
510(4)
A Lattice Version of SHARF
514(11)
Relaxation of the SPR Condition
525(3)
The Undermodelled Case
528(26)
Stationary Points for General Inputs
531(3)
White Noise Inputs Case
534(11)
Problems
545(6)
References
551(3)
Adaptive Notch Filters
554(46)
Introduction
554(2)
Basic Principles
556(6)
Notch Filter Approximations
562(10)
Direct Form Notch Filter
562(4)
Lattice Notch Filter
566(6)
Gradient Discent Algorithms
572(2)
A Simplified Lattice Algorithm
574(12)
Pseudo Least-Squares Algorithms
586(2)
Multiple Sinusoid Case
588(12)
Gradient Descent Algorithms
589(2)
Simplified Lattice Algorithm
591(5)
Problems
596(2)
References
598(2)
Perspectives and Open Problems
600(50)
Convergence in the Undermodelled Case
602(4)
Szego Polynomials
606(6)
Spectrally Weighted L2 Criterion
612(4)
Spectrally Weighted Balanced Systems
616(5)
Weighted Hankel Forms
621(12)
Hankel-Toeplitz Equations
621(3)
Data-Driven Interpretation
624(9)
Spectral Extensions of the Shift Operator
633(17)
Spectrally Weighted Shift Operator
634(8)
Prefiltered Signal Interpretation
642(6)
References
648(2)
Appendix A: Computations with Lattice Filters 650(16)
Appendix B: List of Notations 666(9)
Index 675
Phillip Regalia