Realization of 2-D digital filters via feedback concept

The authors consider a method for realizing a more general class of 2-D systems. The problem of realizing 2-D systems is extended beyond cascade and parallel realizations to include the feedback structure. The restriction on being separable in the denominator is eliminated. However, it is considered a part of the algorithm presented. The method discussed is a decomposition in the frequency domain of a 2-D transfer function into two equivalent general 2-D systems connected in feedback. The idea is then to decompose the 2-D transfer function of the forward and feedback blocks into a pair of 1-D systems having dynamics in different directions. Based on the fact that the parameter of a system cannot be completely stationary for its entire operating life, the feedback realization is introduced to enhance the robustness properties of the filter. Also, the inclusion of feedback structure expands the class of 2-D system realization considered so far in the literature. Both SISO and MIMO realization problems are discussed, and step-by-step algorithms are provided for each case