Improved algorithm to design weighted minimax quadrature mirror filters

Abstract

Recently, it was discovered that the weighted least squares algorithm presented in [1] produced quadrature mirror filters with transition-band anomaly when the transition-band width is wide. This results in sub-optimal solutions. In this paper, we propose an improved weighted least squares algorithm to overcome this problem. In our new method, a term is added to the objective function of the weighted least squares optimization problem. This effectively suppresses the oscillatory components in the transition-band of the resulting filter. Significant improvements in the stop-band attenuation of the filters as well as the overall filter bank responses are achieved for such cases.