SDP Formulation for Design of 2-D Rectangular-Shaped Filters

Abstract

We prose anew technique for the design of linear phase 2-D FIR filter subject to frequency mask constraints, wich can handle filters large enough for practical applications. The designed 2-D filters will admit a fast digital implementation. Moreover, we generalize the trigonometric Markow-Lukacs theorem to enable the 2-D filter specifications to be expressed as semi-definite constrants. As a result, the 2-D filter design problem is then posed as semi-definite program (SDP). In addition, we exploited convex duality to derive equivalent SDP formulation of reduced constraints. Design of 2-D rectangular-shaped filters illustrating the advantages of our method is presented.