Some stability properties of two-dimensional linear shift-invariant digital filters

This paper presents a detailed discussion of stability of twodimensional linear digital filters, and the subtle differences between the one-dimensional and two-dimensional cases. In particular, it is shown that the fact that the impulse response trails off to zero, or more stringently is square summable does not guarantee BIBO (bounded-input-bounded-output) stability. Necessary conditions for the impulse response to be bounded and sufficient conditions for it to be square summable and to approach zero geometrically along any fixed column (or row) are stated.