Iterative Reweighted Minimax Phase Error Designs of IIR Digital Filters With Nearly Linear Phases

Linear phase is an important characteristic of digital filters in many signal processing applications. In this paper, two iterative reweighted minimax phase error algorithms are proposed to design nearly linear-phase infinite impulse response (IIR) digital filters with prescribed or simultaneously minimized magnitude errors and preset transition-band gain. In each iteration of the algorithms, a weighted minimax phase error problem with a fixed weight function is firstly solved using a modified Gauss-Newton method with a variable step length, and the weight function of the phase error is then updated using the square root of a modified envelope of the group-delay error of the filter. With the proposed methods, both very small phase error and group-delay error have been obtained while meeting the requirements on the passband and stopband magnitude errors and the transition-band gain. Design examples demonstrate the effectiveness of the proposed methods and the excellent performance of the designed filters.