Stability of the 2-D Givone-Roesser model with periodic coefficients

Tamal Bose; Mei Qin Chen; Ratchaneekorn Thamvichai

doi:10.1109/TCSI.2006.888666

Stability of the 2-D Givone-Roesser model with periodic coefficients

Tamal Bose
, Mei Qin Chen
, Ratchaneekorn Thamvichai

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

The stability of two-dimensional (2-D) periodically shift varying (PSV) filters formulated as the Givone-Roesser (GR) model is studied. The applications of these filters include processing video signals with cyclostationary noise, image and video scrambling, and design of multiplierless filters. The GR model is embedded into the second model of Fornasini-Marchesisni and the stability of this embedded model is then studied. Several sufficient conditions and one necessary condition are derived for stability. These conditions are compared for their relative computational complexities and their restrictions. Based on the computational complexities of implementing these conditions, an algorithm is proposed to determine the stability of a given 2-D PSV system. Several examples are given to illustrate the results.

Original language	English (US)
Pages (from-to)	566-578
Number of pages	13
Journal	IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Volume	54
Issue number	3
DOIs	https://doi.org/10.1109/TCSI.2006.888666
State	Published - Mar 2007
Externally published	Yes

Keywords

2-D Givone-Roesser model
2-D periodically shift varying filters
Stability

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/TCSI.2006.888666

Cite this

@article{fae5f05c22c54a0f9d6cc9e59b32b5a3,

title = "Stability of the 2-D Givone-Roesser model with periodic coefficients",

abstract = "The stability of two-dimensional (2-D) periodically shift varying (PSV) filters formulated as the Givone-Roesser (GR) model is studied. The applications of these filters include processing video signals with cyclostationary noise, image and video scrambling, and design of multiplierless filters. The GR model is embedded into the second model of Fornasini-Marchesisni and the stability of this embedded model is then studied. Several sufficient conditions and one necessary condition are derived for stability. These conditions are compared for their relative computational complexities and their restrictions. Based on the computational complexities of implementing these conditions, an algorithm is proposed to determine the stability of a given 2-D PSV system. Several examples are given to illustrate the results.",

keywords = "2-D Givone-Roesser model, 2-D periodically shift varying filters, Stability",

author = "Tamal Bose and Chen, \{Mei Qin\} and Ratchaneekorn Thamvichai",

note = "Funding Information: Manuscript received March 9, 2005; revised July 20, 2006. The work of T. Bose work was supported by NASA under Grant NAG5-10716 and the State of Utah Centers of Excellence program. The work of M.-Q. Chen was supported in part by a Citadel Foundation Sabbatical Grant and by the Department of Electrical and Computer Engineering, Utah State University. This paper was recommended by C. Hadjicostis.",

year = "2007",

month = mar,

doi = "10.1109/TCSI.2006.888666",

language = "English (US)",

volume = "54",

pages = "566--578",

journal = "IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications",

issn = "1057-7122",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "3",

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TY - JOUR

T1 - Stability of the 2-D Givone-Roesser model with periodic coefficients

AU - Bose, Tamal

AU - Chen, Mei Qin

AU - Thamvichai, Ratchaneekorn

N1 - Funding Information: Manuscript received March 9, 2005; revised July 20, 2006. The work of T. Bose work was supported by NASA under Grant NAG5-10716 and the State of Utah Centers of Excellence program. The work of M.-Q. Chen was supported in part by a Citadel Foundation Sabbatical Grant and by the Department of Electrical and Computer Engineering, Utah State University. This paper was recommended by C. Hadjicostis.

PY - 2007/3

Y1 - 2007/3

N2 - The stability of two-dimensional (2-D) periodically shift varying (PSV) filters formulated as the Givone-Roesser (GR) model is studied. The applications of these filters include processing video signals with cyclostationary noise, image and video scrambling, and design of multiplierless filters. The GR model is embedded into the second model of Fornasini-Marchesisni and the stability of this embedded model is then studied. Several sufficient conditions and one necessary condition are derived for stability. These conditions are compared for their relative computational complexities and their restrictions. Based on the computational complexities of implementing these conditions, an algorithm is proposed to determine the stability of a given 2-D PSV system. Several examples are given to illustrate the results.

AB - The stability of two-dimensional (2-D) periodically shift varying (PSV) filters formulated as the Givone-Roesser (GR) model is studied. The applications of these filters include processing video signals with cyclostationary noise, image and video scrambling, and design of multiplierless filters. The GR model is embedded into the second model of Fornasini-Marchesisni and the stability of this embedded model is then studied. Several sufficient conditions and one necessary condition are derived for stability. These conditions are compared for their relative computational complexities and their restrictions. Based on the computational complexities of implementing these conditions, an algorithm is proposed to determine the stability of a given 2-D PSV system. Several examples are given to illustrate the results.

KW - 2-D Givone-Roesser model

KW - 2-D periodically shift varying filters

KW - Stability

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DO - 10.1109/TCSI.2006.888666

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EP - 578

JO - IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

JF - IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

IS - 3

ER -

Stability of the 2-D Givone-Roesser model with periodic coefficients

Abstract

Keywords

ASJC Scopus subject areas

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