State-Space Methods

Like 1-D digital filters and other types of systems, 2-D digital filters can be represented in terms of state-space models. In this approach a set of internal signals referred to as state variables is used to describe completely the operation of the filter. The approach has proved very useful in the analysis, design, and implementation of digital filters. It has the advantage that the characterization of the digital filter is in terms of matrices, which are easy to manipulate by means of array or vector processors. State-space models for 2-D digital filters have been proposed by Attasi [ 1 ], Givone and Roesser [ 2 ], and Fornasini and Marchesini [ 3 ]. The model of Givone and Roesser follows naturally from a network theoretic approach and has been used extensively in the past [ 4 ] owing to its generality and relative simplicity. In fact, the models of Attasi and Fornasini and Marchesini can actually be derived from it.