State models and stability for 2-D filters

A generalized 2-D discrete-time filter is considered. Using the concept of a wave advance process, the filter equation is converted to a 1-D recursive form. A 1-D state equation is then developed and a canonical form for the state equation is presented. A norm bound on state transitions is developed, which is then related to the coefficients of the underlying filter equation. The norm bound is used to specify asymptotic stability conditions; the resultant criteria are illustrated through examples.>