Design of two-dimensional recursive digital filters using linear programming

This paper considers the application of linear programming to the design of two-dimensional recursive digital filters. Although the desired specification consists of both magnitude and phase, the design procedure is restricted to the case where the phase specification is linear (i.e., constant group delay). A stability constraint that is linear in form and which enables the design of a class of stable nonsymmetric half-plane (NSHP) and quarter-plane filters (QP) is proposed and proof of the sufficiency of the stability constraint is also provided. Examples of NSHP and QP stable filter designs using linear programming that incorporate the linear stability constraint are presented. Some examples of applications to image processing are also provided.