On an Alternative Parameterization of the Solutions of the Partial Realization Problem

The solutions of the partial realization problem have to satisfy a finite number of interpolation conditions at [infinity]. The minimal degree of an interpolating deterministic system is called the algebraic degree or McMillan degree of the partial covariance sequence and is easy to compute. The sol...

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Bibliographic Details
Published in:Acta applicandae mathematicae 2000-05, Vol.61 (1-3), p.317
Main Authors: Tony Van Gestel, Marc Van Barel, De Moor, Bart
Format: Article
Language:English
Subjects:
Algebra
Codes
Fourier transforms
Mathematics
Noise
Signal processing
Studies
Theory
Online Access:Get full text
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Summary:The solutions of the partial realization problem have to satisfy a finite number of interpolation conditions at [infinity]. The minimal degree of an interpolating deterministic system is called the algebraic degree or McMillan degree of the partial covariance sequence and is easy to compute. The solutions of the partial stochastic realization problem have to satisfy the same interpolation conditions and have to fulfill a positive realness constraint. The minimal degree of a stochastic realization is called the positive degree. In the literature, solutions of the partial realization problem are parameterized by the Kimura-Georgiou parameterization. Solutions of the partial stochastic realization problem are then obtained by checking the positive realness constraint for the interpolating solutions of the corresponding partial realization problem. In this paper, an alternative parameterization is developed for the solutions of the partial realization problems. Both the solutions of the partial and partial stochastic realization problem are analyzed in this parameterization, while the main concerns are the minimality and the uniqueness of the solutions. Based on the structure of the parameterization, a lower bound for the positive degree is derived. [PUBLICATION ABSTRACT]
ISSN:0167-8019
1572-9036
DOI:10.1023/a:1006405104724