A set of necessary stability conditions for \(m\)-D nonlinear digital filters
type: Item
instance of: scholarly article
title: A set of necessary stability conditions for \(m\)-D nonlinear digital filters
zbMATH Open document ID: 0833.93041
DOI: 10.1007/BF01260337
author: Peter H. Bauer
published in: Circuits, Systems, and Signal Processing
publication date: 1996-03-11T00:00:00Z
review text: The intrinsic feature of the so-called \(m\)-D systems is that these propagate information in \(m\) separate directions, for example, \(i_1, i_2, \dots, i_m\). Here asymptotic stability of possibly nonlinear, recursive, first hyperquadrant causal (non-singular) \(m\)-D digital systems (filters) is considered. Instead of a given \(m\)-D system, its projections on all possible direction subsets \(\{j_1, j_2, \dots, j_\upsilon\} \subset \{i_1, i_2, \dots, i_m \}\), \(1\leq \nu< m\), termed \(\nu\)-D subsystems (projections), are examined. This is clearly a considerable simplification of a system structure so that only necessary conditions may be provided. In effect, a total of \(2^m -2\) necessary conditions is developed, \(m\) of which are of 1-D nature. The author refers also his results to the well known notion of the so-called practical stability introduced by Agathoklis and Burton.
Mathematics Subject Classification ID: 93C62
Mathematics Subject Classification ID: 93C35
Mathematics Subject Classification ID: 93D20
zbMATH DE Number: 798727
zbMATH Keywords: asymptotic stability
zbMATH Keywords: \(m\)-D digital systems
zbMATH Keywords: practical stability
reviewed by: Krzysztof Gałkowski
MaRDI profile type: Publication
cites work: Q3474575
cites work: Finite word-length effects in m-D digital filters with singularities on the stability boundary
cites work: A stability analysis of two-dimensional nonlinear digital state-space filters
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cites work: Q4875338
cites work: Two-dimensional digital filters without overflow oscillations and instability due to finite word length
full work available at URL: https://doi.org/10.1007/bf01260337
OpenAlex ID: W2002659140
description: scientific article; zbMATH DE number 798727