**Authors: **Billye Cheek Mieczyslaw Dabkowski Amr El Nagdi Louis R Hunt T P LaFave Ke Liu Duncan L MacFarlane Viswanath Ramakrishna

**Publish Date**: 2012/02/10

**Volume:** 118, **Issue:** 1, **Pages:** 107-123

## 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

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