Design of linear-phase quadrature mirror filters with powers-of-two coefficients

This paper considers the design of linear-phase quadrature mirror filters (QMF´s) with powers-of-two coefficients. A design method based on a recently developed weighted least-squares (WLS) algorithm is presented. First, we design QMF´s with continuous coefficients using the WLS algorithm. This design process provides two favorable design results that the prototype analysis filter has quasi-equiripple stopband response and the resulting QMF bank shows quasi-equiripple reconstruction error behavior. To avoid the effect of nonuniformly distributed coefficient grid due to discretization of the filter coefficients, a procedure is then performed for obtaining an appropriate filter gain factor. Finally, utilizing the resulting error weighting function obtained by the WLS algorithm, we propose an efficient discrete optimization process to obtain a discrete solution in the minimax optimal sense. Design examples demonstrating the effectiveness of the proposed method are included