New linear-programming-based filter design

It is well known that the filter-design problem with mask constraints can be formulated as a semi-infinite program. There are two approaches toward the solution of this semi-infinite program. The first griding approach relaxes the semi-infinite constraint by refining it in the finite griding domain so it does not always guarantee global optimal and feasible solution. The second semi-definite programming (SDP)-based approach does guarantee the global optimal solution and excellently handles positive real constraints. However, the magnitude constraints are still persistent and not yet handled by SDP tool in an efficient manner. In this brief, a new tight polyhedral approximation for semi-infinite constrained domain is proposed. Based on it, we present a new linear-programming-based solution method for filter design, which unlike the griding approach yields global solution and unlike SDP based approach is practical for even long-tap filters. Simulation results confirm the viability of the proposed method.