In many signal filtering applications

the requirement on the magnitude response of the filter is higher than that on the phase response. The design of magnitude-response constrained finite impulse response (FIR) filters was considered and a minimax weighted phase error design method was proposed. Replacing the nonconvex magnitude error constraint with an elliptic error constraint makes the design problem a convex one. Incorporating with a bisection technique

a design algorithm was firstly obtained for the case with a preset phase-error weight. Using this algorithm as the iteration core

an iterative reweighted minimax phase error design algorithm was constructed

where the phase-error weight is not fixed but updated using a modified envelop of the group-delay error function. After the iterative algorithm converges

the resultant filter has a near equiripple group-delay error and a reduced maximum group-delay error. Experiments demonstrate that the proposed method has obtained smaller passband phase error and group-delay error than the existing phase-error constrained minimax magnitude error method.