Asymptotic stability of linear shift-invariant two-dimensional digital filters

A theory of asymptotic stability is developed for a large class of linear shift-invariant half-plane 2-D digital filters. The theory is based on a spatial-domain representation consisting of a 1-D difference equation with coefficients in an algebra of 1-D functions. Various necessary and sufficient conditions are derived for asymptotic stability. In particular, it Is shown that stability testing for both quarter- and half-plane 2-D filters reduces to determining the invertibility of a matrix whose entries are in an algebra of 1-D functions. These results are related to existing frequencydomain criteria for stability.