Minimax Design of M-D Complex-Coefficient FIR Filters with Nearly-Constant Low Group Delays

The optimal designs of multi-dimensional (M-D) complex-coefficient finite-extent impulse response (FIR) filters with low group delays predominantly consider only the minimization of the frequency response error. This leads to substantial deviation of the group delay from the desired constant group delay of such a filter, especially near the passband edges. In this paper, we propose a minimax design method for M-D complex-coefficient FIR filters with reduced group delay error. We incorporate constraints on phase response error while minimizing the frequency response error. We formulate the proposed minimax design method as a second-order cone programming problem. Design examples confirm that the proposed minimax design method significantly reduces the group delay error compared to previously proposed methods.