Analysis of a Polynomial System Arising in the Design of an Optical Lattice Filter Useful in Channelization

Autor:	Amr El Nagdi, Mieczyslaw K. Dabkowski, Tim LaFave, Viswanath Ramakrishna, Ke Liu, Billye Cheek, Louis R. Hunt, Duncan L. MacFarlane
Rok vydání:	2012
Předmět:	Matrix (mathematics) Signal processing Polynomial State-space representation Discrete time and continuous time Applied Mathematics Filter (signal processing) Topology Bézout's theorem Mathematics Characteristic polynomial
Zdroj:	Acta Applicandae Mathematicae. 118:107-123
ISSN:	1572-9036 0167-8019
DOI:	10.1007/s10440-012-9680-8
Popis:	In this work, we consider design questions for an active optical lattice filter, which is being manufactured at the University of Texas at Dallas, and which has proven to be useful in the signal processing task of RF channelization. The filter can be described by a linear, discrete time state space model. The controlling agents, the gains, are embedded in the matrices intervening in this state space model. Consequently, techniques from linear feedback control theory do not apply. We concentrate on the question of finding real valued gains so that the A matrix of the state space model has a prescribed characteristic polynomial. We find that three of the coefficients can be arbitrarily picked, but that the remaining are constrained by these and the other system parameters. Our techniques use methods from constructive algebraic geometry.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8904870e982d1ab4ae2c932448dc3b7b https://doi.org/10.1007/s10440-012-9680-8 Zobrazit plný text záznamu Plný text ve formátu PDF