Design of 2-D digital filters with an arbitrary response and no overflow oscillations based on a new stability condition

This paper presents a new optimal-design-oriented stability condition for 2-D state-space digital filters. A general formulation for optimal design of 2-D recursive digital filters is obtained by applying the new condition. The formulation can be reduced into an unconstrained minimization problem and be used to design 2-D state-space digital filters with an arbitrary response. Furthermore, the resulting filters are guaranteed to be not only stable but also able to suppress overflow oscillations due to adder overflows. Some practical design techniques for the spatialdomain specifications and the frequency-domain specifications are proposed on the basis of the general formulation. Several examples are given to show the effectiveness of the proposed techniques.