Algebraic approach to discrete-time polynomial spectral factorization

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MI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryグローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」In this paper we propose an algebraic approach to the discrete-time polynomial spectral factorization problem, which has a signi cant importance in signal processing and control for nite dimensional linear systems. We also attempt to generalize the approach and establish a new framework of symbolic optimization of algebraic functions that is relevant to possibly a wide variety of practical application areas. The crucial aspects of the framework are the suitable use of algebraic methods coupled with the discovery and exploitation of structural properties of the problem in the conversion process into the framework, and the feasibility of algebraic methods when performing the optimization. Two examples are also included to demonstrate the signi cance and relevance of the proposed approach and framework.
2009-04-08