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Multidimensional Systems and Signal Processing

, Volume 28, Issue 1, pp 305–314 | Cite as

On minimal realizations of first-degree 3D systems with separable denominators

  • Thi Loan Nguyen
  • Li Xu
  • Zhiping Lin
  • David B. H. Tay
Article

Abstract

In this paper, we focus on first-degree three-dimensional (3D) causal systems which have separable denominators. Gröbner basis is applied to prove that not all first-degree 3D systems with separable denominators have minimal realizations (of order 3). This is in contrast to 2D systems with separable denominators which always admit absolutely minimal realizations. Two illustrative examples are presented.

Keywords

Multidimensional systems State space realization Minimal realization  Gröbner basis 

Notes

Acknowledgments

We wish to acknowledge the funding support for this project from Nanyang Technological University under the Undergraduate Research Experience on Campus (URECA) program.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Thi Loan Nguyen
    • 1
  • Li Xu
    • 2
  • Zhiping Lin
    • 3
  • David B. H. Tay
    • 4
  1. 1.School of Physics and Mathematics SciencesNanyang Technological UniversitySingaporeSingapore
  2. 2.Department of Electronics and Information SystemsAkita Prefectural UniversityAkitaJapan
  3. 3.School of EEENanyang Technological UniversitySingaporeSingapore
  4. 4.Department of EngineeringLaTrobe UniversityBundooraAustralia

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