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

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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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Acknowledgement

The authors gratefully acknowledge the support of the Defense Advanced Research Project Agency (DARPA) through grant No. HR0011-8-1-005.

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Authors and Affiliations

  1. Mathematical Sciences, University of Texas at Dallas, P.O. Box 830688, Richardson, TX, 75083, USA

    Billye Cheek, Mieczyslaw Dabkowski & Viswanath Ramakrishna

  2. Electrical Engineering, University of Texas at Dallas, P.O. Box 830688, Richardson, TX, 75083, USA

    Amr El Nagdi, Louis R. Hunt, T. P. LaFave Jr, Ke Liu & Duncan L. MacFarlane

Authors
  1. Billye Cheek
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  2. Mieczyslaw Dabkowski
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  3. Amr El Nagdi
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  4. Louis R. Hunt
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  5. T. P. LaFave Jr
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  6. Ke Liu
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  7. Duncan L. MacFarlane
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  8. Viswanath Ramakrishna
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Corresponding author

Correspondence to Viswanath Ramakrishna.

Additional information

This paper is dedicated to Professor Goong Chen, on the occasion of his 60th birthday. He has been a wonderful colleague of, and an astute mentor to, the corresponding author.

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Cheek, B., Dabkowski, M., El Nagdi, A. et al. Analysis of a Polynomial System Arising in the Design of an Optical Lattice Filter Useful in Channelization. Acta Appl Math 118, 107–123 (2012). https://doi.org/10.1007/s10440-012-9680-8

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  • DOI: https://doi.org/10.1007/s10440-012-9680-8

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