STABILITY OF 2-DIMENSIONAL DISCRETE-SYSTEMS WITH PERIODIC COEFFICIENTS

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 pro cessing 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 c oefficients. This PSV model is then studied for stability. Two suffici ent conditions and one necessary condition are established for asympto tic stability. Some examples are given to illustrate the results.