Linear phases are often a requisite in many signal filtering applications. All-pass digital filters are the main device to realize the linear phases. An iterative reweighted minimax method is proposed for the design of all-pass digital filters. The method minimizes the maximum weighted phase deviation from some linear phase

and reduces the maximum group-delay deviation from some constant group delay through updating the phase-error weight function iteratively by virtue of the group-delay deviation. To demonstrate its advantages

the proposed method is applied in the designs of phase equilizers and linear-phase Hilbert transformers. Simulation results show that the proposed algorithm has good convergence properties

and is very effective in realizing the nearly linear phase and nearly constant group delay of the filtering system.