An Operator Perspective on Signals and Systems [recurso electrónico] / by Arthur E. Frazho, Wisuwat Bhosri.
Tipo de material:
TextoSeries Operator Theory: Advances and Applications, Linear Operators and Linear Systems ; 204Editor: Basel : Birkhäuser Basel, 2010Descripción: XI, 431 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783034602921Tema(s): Mathematics | Operator theory | Systems theory | Computer science | Mathematics | Operator Theory | Systems Theory, Control | Computational Science and EngineeringFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 515.724 Clasificación LoC:QA329-329.9Recursos en línea: Libro electrónico
| Tipo de ítem | Biblioteca actual | Colección | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras |
|---|---|---|---|---|---|---|---|
| Libro Electrónico | Biblioteca Electrónica | Colección de Libros Electrónicos | QA329 -329.9 (Browse shelf(Abre debajo)) | 1 | No para préstamo | 373014-2001 |
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| QA329 -329.9 Recent Advances in Operator Theory in Hilbert and Krein Spaces | QA329 -329.9 Characteristic Functions, Scattering Functions and Transfer Functions | QA329 -329.9 Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations | QA329 -329.9 An Operator Perspective on Signals and Systems | QA329 -329.9 A Glimpse at Hilbert Space Operators | QA329 -329.9 Recent Trends in Toeplitz and Pseudodifferential Operators | QA329 -329.9 Noncommutative Functional Calculus |
Basic Operator Theory -- The Wold Decomposition -- Toeplitz and Laurent Operators -- Inner and Outer Functions -- Rational Inner and Outer Functions -- The Naimark Representation -- The Rational Case -- Finite Section Techniques -- The Levinson Algorithm and Factorization -- Isometric Representations and Factorization -- Signal Processing -- Riccati Methods -- Riccati Equations and Factorization -- Kalman and Wiener Filtering -- Interpolation Theory -- Tangential Nevanlinna-Pick Interpolation -- Contractive Nevanlinna-Pick Interpolation -- Appendices -- A Review of State Space -- The Levinson Algorithm.
In this monograph, we combine operator techniques with state space methods to solve factorization, spectral estimation, and interpolation problems arising in control and signal processing. We present both the theory and algorithms with some Matlab code to solve these problems. A classical approach to spectral factorization problems in control theory is based on Riccati equations arising in linear quadratic control theory and Kalman ?ltering. One advantage of this approach is that it readily leads to algorithms in the non-degenerate case. On the other hand, this approach does not easily generalize to the nonrational case, and it is not always transparent where the Riccati equations are coming from. Operator theory has developed some elegant methods to prove the existence of a solution to some of these factorization and spectral estimation problems in a very general setting. However, these techniques are in general not used to develop computational algorithms. In this monograph, we will use operator theory with state space methods to derive computational methods to solve factorization, sp- tral estimation, and interpolation problems. It is emphasized that our approach is geometric and the algorithms are obtained as a special application of the theory. We will present two methods for spectral factorization. One method derives al- rithms based on ?nite sections of a certain Toeplitz matrix. The other approach uses operator theory to develop the Riccati factorization method. Finally, we use isometric extension techniques to solve some interpolation problems.
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