Two-dimensional digital filters without overflow oscillations and instability due to finite word length

Tzafestas, Spyros G.; Kanellakis, A.; Theodorou, N. J.

doi:10.1109/78.157230

Cited by 41 publications

(23 citation statements)

References 24 publications

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“…Based on this background together with [5], [7], [ 13] and [ 18], we discuss the aforementioned three problems in the subsequent sections.…”

Section: I ) = [ C1 C2 C ] X ( I L I 2 I mentioning

confidence: 99%

“…Further, these results can be extended to n-D systems as well. Therefore, in the second part of this paper, we extend the results of [6] and [7] to n-D case, and derive some tight lower bounds on coefficient wordlength I lk)r n-D systems,…”

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confidence: 97%

“…Recently, Tzafestas e t a L [7] extended the I -D result of [6] to 2-D case and obtained a lower bound on coefficient wordlength I for stable 2-D digital systems. Their results are useful; however, the bounds are conservative and can be considerably improved if the system transition matrix A has certain forms.…”

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confidence: 98%

“…In the third part of this paper, we present some further results on the asymptotic stability based on [7] and [t 3].…”

mentioning

confidence: 99%

“…The Mird problem, which is the (global) asymptotic stability, has attracted extensive attention in the last two decades, many results have been carried out, see [7]- [15] and the references therein. In the third part of this paper, we present some further results on the asymptotic stability based on [7] and [t 3].…”

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confidence: 99%

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Stability results for decomposable multidimensional digital systems based on the lyapunov equation

Xiao

Hill

1996

Multidim Syst Sign Process

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Abstract. Lower bounds for the stability margins of 2-D digital systems are extended to n-D systems. These bounds are then improved f?)r n-D (including 2-D) systems which have characteristic polynomials with I-D factor polynomials. Stability analysis of n-D systems due to finite wordlength is considered, some tight lower bounds oll coefficient wordlength which guarantee the n-D system to be stable and/or globally asymptotically stable are presented. Improved and/or extended criteria for absence of overflow oscillations and global asymptotic stability of n-D systems are proposed as well. An example is presented to illustrate the theoretical results, and it is shown that the lower bound on coefficient wordlength could be considerably improved for the (partial) factorable denominator n-D digital systems. All the discussions are based on the n-D Lyapunov equation.Key Words: Multidimensional systems, Stability margins, Finite wordlength effect, Overflow oscillations, Limit cycles, Asymptotic stability I n t r o d u c t i o nStability of multidimensional (n-D) digital systems is an essential requirement for the design and implementation of such systems. From a practical point of view, however, designers are not only interested whether an n-D system is stable or not in theory, but also interested in the following three important stability problems:1. How far is a stable n-D system from being unstable, i.e., what is the stability margin of the n-D system? 2. When a stable n-D system is implemented with finite wordlength machines, how many bits of coefficient wordlength should be used to guarantee the n-D system to be stable?3. Does the n-D digital system have the absence of limit cycles (or overflow oscillations) due to finite word length?Concerning the first problem, the stability margin of 2-D systems was defined in [ 1 ], then it was extended to the n-D case in [2]. Algorithms for calculating the stability margins of n-D systems were presented in [ 1 ]- [4]. These results, however, were carried out in the frequency domain. In [5], Agathoklis proposed a method, based on the 2-D Lyapunov equation, to estimate lower bounds for the stability margin of 2-D digital systems. In the first part of

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“…Based on this background together with [5], [7], [ 13] and [ 18], we discuss the aforementioned three problems in the subsequent sections.…”

Section: I ) = [ C1 C2 C ] X ( I L I 2 I mentioning

confidence: 99%

mentioning

confidence: 97%

mentioning

confidence: 98%

“…In the third part of this paper, we present some further results on the asymptotic stability based on [7] and [t 3].…”

mentioning

confidence: 99%

mentioning