### Abstract

The recent interest in delta-operator (or, δ-operator) formulated discrete-time systems (or, δ-systems) is due mainly to (a) their superior finite wordlength characteristics as compared to their more conventional shift-operator (or, q-operator) counterparts (or, q-systems), and (b) the possibility of a more unified treatment of both continuous- and discrete-time systems. With such advantages, design, analysis, and implementation of two-dimensional (2-D) discrete-time systems using the δ-operator is indeed warranted. Towards this end, the work in this paper addresses the development of an easily implementable direct algorithm for stability checking of 2-D δ-system transfer function models. Indirect methods that utilize transformation techniques are not pursued since they can be numerically unreliable. In developing such an algorithm, a tabular form for stability checking of δ-system characteristic polynomials with complex-valued coefficients and certain quantities that may be regarded as their corresponding Schur-Cohn minors are also proposed.

Original language | English |
---|---|

Pages (from-to) | 287-312 |

Number of pages | 26 |

Journal | Multidimensional Systems and Signal Processing |

Volume | 6 |

Issue number | 4 |

DOIs | |

State | Published - Oct 1 1995 |

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### Keywords

- δ-operator formulated discrete-time systems
- bivariate polynomials
- Schur-Cohn minors
- stability
- two-dimensional digital filters
- Two-dimensional discrete-time systems

### ASJC Scopus subject areas

- Theoretical Computer Science
- Electrical and Electronic Engineering
- Signal Processing
- Computational Theory and Mathematics

### Cite this

**An algorithm for stability determination of two-dimensional delta-operator formulated discrete-time systems.** / Premaratne, Kamal; Boujarwah, A. S.

Research output: Contribution to journal › Article

*Multidimensional Systems and Signal Processing*, vol. 6, no. 4, pp. 287-312. https://doi.org/10.1007/BF00983557

}

TY - JOUR

T1 - An algorithm for stability determination of two-dimensional delta-operator formulated discrete-time systems

AU - Premaratne, Kamal

AU - Boujarwah, A. S.

PY - 1995/10/1

Y1 - 1995/10/1

N2 - The recent interest in delta-operator (or, δ-operator) formulated discrete-time systems (or, δ-systems) is due mainly to (a) their superior finite wordlength characteristics as compared to their more conventional shift-operator (or, q-operator) counterparts (or, q-systems), and (b) the possibility of a more unified treatment of both continuous- and discrete-time systems. With such advantages, design, analysis, and implementation of two-dimensional (2-D) discrete-time systems using the δ-operator is indeed warranted. Towards this end, the work in this paper addresses the development of an easily implementable direct algorithm for stability checking of 2-D δ-system transfer function models. Indirect methods that utilize transformation techniques are not pursued since they can be numerically unreliable. In developing such an algorithm, a tabular form for stability checking of δ-system characteristic polynomials with complex-valued coefficients and certain quantities that may be regarded as their corresponding Schur-Cohn minors are also proposed.

AB - The recent interest in delta-operator (or, δ-operator) formulated discrete-time systems (or, δ-systems) is due mainly to (a) their superior finite wordlength characteristics as compared to their more conventional shift-operator (or, q-operator) counterparts (or, q-systems), and (b) the possibility of a more unified treatment of both continuous- and discrete-time systems. With such advantages, design, analysis, and implementation of two-dimensional (2-D) discrete-time systems using the δ-operator is indeed warranted. Towards this end, the work in this paper addresses the development of an easily implementable direct algorithm for stability checking of 2-D δ-system transfer function models. Indirect methods that utilize transformation techniques are not pursued since they can be numerically unreliable. In developing such an algorithm, a tabular form for stability checking of δ-system characteristic polynomials with complex-valued coefficients and certain quantities that may be regarded as their corresponding Schur-Cohn minors are also proposed.

KW - δ-operator formulated discrete-time systems

KW - bivariate polynomials

KW - Schur-Cohn minors

KW - stability

KW - two-dimensional digital filters

KW - Two-dimensional discrete-time systems

UR - http://www.scopus.com/inward/record.url?scp=0029394578&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029394578&partnerID=8YFLogxK

U2 - 10.1007/BF00983557

DO - 10.1007/BF00983557

M3 - Article

VL - 6

SP - 287

EP - 312

JO - Multidimensional Systems and Signal Processing

JF - Multidimensional Systems and Signal Processing

SN - 0923-6082

IS - 4

ER -