Design of WLS FIR filters with group delay constraint

This paper presents a weighted least-squares method for the design of real coefficient finite impulse response digital filters with arbitrary magnitude and group delay responses. To meet with both the prescribed magnitude response and group delay, a complex magnitude constraint and an explicit group delay constraint are imposed in the design formulation. Through analytical derivation of the group delay and its gradient, the group delay error is linearized by a sequence of approximations, each of which can be cast and solved efficiently in the second-order cone programming (SOCP) framework.