Theory and Design of Linear-Phase Minimax FIR Filters with Mixed Constraints in the Frequency Domain

The alternation theorem is the core of efficient approximation algorithms for the minimax design of finite-impulse response (FIR) filters. In this paper, an extended alternation theorem with additional mixed constraints, i.e., equality-and-inequality constraints, is obtained. Then, an efficient multiple-exchange algorithm based on the extended theorem is presented for designing linear-phase FIR filters with frequency mixed constraints in the minimax sense. Further, convergence of the algorithm is established. Several design examples and comparisons with existing techniques are presented, and the simulation results show that the proposed algorithm is numerically more efficient and guaranteed to converge to the optimal solution.