Phase compensation for multichannel low-frequency response using minimax approximation

For a multichannel loudspeaker system, the selection of crossover frequency between the subwoofer and satellite loudspeakers is essential for reconstructing a nearly perfect sound field in the reverberation room. Apart from the distortion-free of individual loudspeakers, the overall spectral variation between the subwoofer and satellite loudspeakers should be minimized around the selected crossover frequency. In this work, we propose a phase compensation scheme based on the minimax approximation to flatten the spectral response around the crossover frequency for the loudspeaker system emphasized on the low-frequency effect. The cascaded all-pass filter is shown to yield an improved low-frequency performance by flattening the net magnitude response in the crossover region. As a result, one example of numerical design based on a reverberant room recording is shown to demonstrate the usefulness of our approach.