Design and implementation of two-dimensional fully recursive digital filters

The two-dimensional (2-D) fully recursive filter was recently introduced by the authors as a more general 2-D recursive filter. In this paper, we present a design algorithm and an implementation method for this class of filters. The design algorithm incorporates a novel stability test. We discuss the boundary condition problem which occurs in the implementation of fully recursive filters. We propose a direct fully recursive implementation method which has been verified in software. Several design examples and comparisons are provided.