Details:
Title  Analysis of a polynomial system arising in the design of an optical lattice filter useful in channelization.  Author(s)  Billye Cheek, Mieczyslaw Dabkowski, Louis R. Hunt, T.P. jun. LaFave, Ke Liu, Duncan L. MacFarlane, Amr El Nagdi, Viswanath Ramakrishna  Type  Article in Journal  Abstract  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.  Keywords  Channelizers, Photonics, Groebner bases, Bezout’s theorem  ISSN  01678019; 15729036/e 
URL 
http://link.springer.com/article/10.1007%2Fs1044001296808 
Language  English  Journal  Acta Appl. Math.  Volume  118  Number  1  Pages  107123  Publisher  Springer Netherlands, Dordrecht  Year  2012  Edition  0  Translation 
No  Refereed 
No 
