Stability of two-dimensional discrete systems with periodic coefficients

Abstract

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.

Spectrum of periodically correlated fields

“…A summary of the theory of PC sequences can be found in [23]. Surprisingly, there are only several works [2,3,4,6,7,10,11,21,36] dealing with PC fields, and each one concentrates on a particular type, namely coordinate-wise strong periodicity. An intention of this paper is to sketch a unified theory of fields over any locally compact Abelian (LCA) group G which are periodically correlated with respect to an arbitrary closed subgroup K of G. We emphasize the case of G = Z n ×R m to illustrate the results.…”

Stability of 2-D periodic state-space filters

“…They have been designed and employed in various image processing appli cations such as multirate filter banks and image scrambling. However, the stability of 2-D PSV filters implemented as state-space models has not received much attention [1]- [3].…”

“…Note that matrices A(i,j ) and B(i,j) are also periodic with period (P, Q). The model of (3) will be used to obtain stability [3] and the proofs are therefore omit ted. Throughout the paper, let P = Sp and Q = Sq where p, q are positive integers, and S is the greatest common di visor of P and Q.…”

“…In [3], 2-D PSV filters fonnulated as the 2n d model of Fornasini-Marchesini (PM) were consid ered for stability directly and some conditions were estab lished. In this paper, The stability of 2-D PSV filters re alized as the Givone-Roesser (OR) model is studied.…”