Design of allpass IIR digital filters using a minimax frequency response error method

The design of allpass infinite impulse response (IIR) digital filters is usually to minimize the maximum or weighted square sum of the phase response error since the magnitude response of the filter is constant over the whole frequency band. Considering that the magnitude of the frequency response error of an allpass filter is a monotonic function of its absolute phase response error, this paper applies the minimax frequency response error design methods for general IIR filters to the design of allpass IIR filters. By using the specific form of the frequency response of an allpass IIR filter in design methods for general IIR filters, this paper obtains three kinds of new algorithms for the minimax design of allpass IIR filters. In order to reduce the group delay error of the designed filters, the envelope of the group delay error is used to reweight the frequency response error, resulting in near equiripple group delay error response with a much smaller maximum value. Design examples demonstrate the feasibility and effectiveness of the proposed methods.