Analysis of 2-D state-space periodically shift-variant discrete systems

Rajan, Sreeraman; Joo, Kyung Sub; Bose, T.

doi:10.1007/bf01182594

Cited by 10 publications

(4 citation statements)

References 14 publications

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“…Since the system is assumed stable, . Thus the (15) implies that Note that the matrices use the same coefficient matrices with indices in by shifting indices each other. So can be simplified further.…”

Section: Stability Of the 2-d Psv Systemmentioning

confidence: 99%

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Stability of two-dimensional discrete systems with periodic coefficients

Bose

Chen

Joo

et al. 1998

IEEE Trans. Circuits Syst. II

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Two-dimensional (2-D) discrete systems with periodic coefficients are considered for stability. These systems are called periodically shift variant (PSV) digital filters and have many applications in signal processing that include the filtering of 2-D signals with cyclostationary noise, scrambling of digital images, and implementation of multirate filter banks. In this paper, the filters are formulated in the form of the well known Fornasini-Marchesini state-space model with periodic coefficients. This PSV model is then studied for stability. Two sufficient conditions and one necessary condition are established for asymptotic stability. Some examples are given to illustrate the results. Mei-Qin Chen received the B.S. degree in mathematics from Eastern Illinois University in 1983 and the M.S. and Ph.D. degrees in mathematics from the University of Illinois at Champaign-Urbana in 1985 and 1989, respectively.

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Section: Stability Of the 2-d Psv Systemmentioning

confidence: 99%

“…These structures are useful for analysis, but are computationally intensive for implementation. In [14] and [15], 2-D PSV systems were considered and new shift-invariant structures were derived. These structures are computationally efficient and lend themselves to easier analysis.…”

Section: Introductionmentioning

confidence: 99%

Stability of two-dimensional discrete systems with periodic coefficients

Bose

Chen

Joo

et al. 1998

IEEE Trans. Circuits Syst. II

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“…Harris deconvoluted the blurring due to atmospheric turbulence in telescope images in [17]. In addition, the inverse filtering problem of shift-variant imaging systems was discussed in [24], the technique of blind deconvolution is applied in [27], and invertibility of 2-D state-space periodically shift-variant discrete systems was studied in [25].…”

Section: Introductionmentioning

confidence: 99%

H∞ deconvolution filtering of 2-d digital systems

Xie

Zhang

et al. 2002

IEEE Trans. Signal Process.

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This paper deals with the problem of two-dimensional (2-D) digital system deconvolution under the performance specification. The 2-D digital system under consideration is expressed by the Fornasini-Marchesini local state-space (FM LSS) model. For a given 2-D digital system, a 2-D deconvolution filter is designed to reconstruct the 2-D signal to meet a prescribed performance specification. A key analytical means for the deconvolution filter design is the 2-D bounded realness property derived in this paper. Applying this property, the 2-D deconvolution filter design is formulated into a convex optimization problem characterized by linear matrix inequalities (LMIs). A procedure for the design of an deconvolution filter for a given 2-D digital system with measurement noise is developed first. The LMI approach to the 2-D deconvolution filtering problem is further extended to the 2-D robust deconvolution filtering problem with polytopic modeling uncertainties in the 2-D system. The obtained results on the 2-D deconvolution filtering and robust deconvolution filtering problems are demonstrated with examples.

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“…With the purpose of obtaining an invariant formulation of (11), following the ideas of [5], we now define lifted versions of the horizontal and vertical states as:…”

Section: Invariant Formulationsmentioning

confidence: 99%

Roesser model representation of 2D periodic behaviors: the (2,2)-periodic SISO case

Aleixo

Rocha

2017

2017 10th International Workshop on Multidimensional (nD) Systems (nDS)

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In this paper we consider 2D single-input/singleoutput behaviors described by linear partial difference equations with (2,2)-periodically varying coefficients, and present a method to obtain 2D Roesser state-space representations (or realizations) for such behaviors. Since these cannot be obtained by separately realizing each shiftinvariant system resulting from "freezing" the varying coefficients, we propose a method based on the realization of an invariant input/output behavior obtained by suitably "lifting" the trajectories of the original periodic behavior.

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Analysis of 2-D state-space periodically shift-variant discrete systems

Cited by 10 publications

References 14 publications

Stability of two-dimensional discrete systems with periodic coefficients

Stability of two-dimensional discrete systems with periodic coefficients

H∞ deconvolution filtering of 2-d digital systems

Roesser model representation of 2D periodic behaviors: the (2,2)-periodic SISO case

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