Stability of the 2-D Givone–Roesser Model With Periodic Coefficients

The stability of two-dimensional (2-D) periodically shift varying (PSV) filters formulated as the Givone-Roesser (GR) model is studied. The applications of these filters include processing video signals with cyclostationary noise, image and video scrambling, and design of multiplierless filters. The GR model is embedded into the second model of Fornasini-Marchesisni and the stability of this embedded model is then studied. Several sufficient conditions and one necessary condition are derived for stability. These conditions are compared for their relative computational complexities and their restrictions. Based on the computational complexities of implementing these conditions, an algorithm is proposed to determine the stability of a given 2-D PSV system. Several examples are given to illustrate the results