Improved weighted least squares algorithm for the design of quadrature mirror filters

This paper presents an improved weighted least squares (WLS) algorithm for the design of quadrature mirror filters (QMF's). First, a new term is incor porated into the objective function that effectively prevents an optimizati on algorithm from producing suboptimal QMF's, These suboptimal QMF's exhibi t transition band anomaly; the frequency responses of the filters have larg e oscillatory components in the transition band. The new term can be applie d to the WLS design of any FDR tilter to prevent similar transition band an omaly. Next, we present the algorithm to obtain the QMF coefficients that m inimizes the objective function incorporating the new term. The computation al requirement of this algorithm is also briefly discussed. Last, we includ e a set of practical design rules for use with our algorithm. These rules s implify the design process by providing good estimation of the design param eters, such as the minimum filter length, to meet a given set of QMF specif ications.