Optimal Design of 2--D Digital Filters Based on a New Stability Condition of 2--D Discrete Spatial Systems.

Most of the literatures dealing with the design of 2-D digital filters, have considered design problems for the restricted structures. This is because it is difficult to test the stability of general 2-D digital filter structures. Thus, globally optimal 2-D digital filters are difficult to design. This paper presents a necessary and sufficient condition for the asymptotic stability of 2-D spatial systems represented by the local state-space model. Also, the relationship between model parameters and stability is shown. The optimal design of 2-D digital filters generally is formulated on the basis of the stability condition. The optimal design is reduced further into an unconstrained nonlinear minimization problem. The design method for 2-D spatial domain specifications is proposed as a special case of the formulation. Numerical examples are given to illustrate the effectiveness of the method. Finally, the new optimization algorithm for the design is considered. [ABSTRACT FROM AUTHOR]