DESIGN OF QUADRATURE MIRROR FILTERS WITH LINEAR-PHASE IN THE FREQUENCY-DOMAIN

This paper considers the design of quadrature mirror filter (QMF) banks whose analysis and synthesis filters have linear phase. Due to the fact that the design problem in the frequency domain is a highly nonlinear optimization problem in the least square sense, we propose a linearization technique to reformulate the design problem so that the core work in finding the optimal filter coefficients at each iteration is to solve a set of linear equations. Therefore, an analytical solution formula can be obtained. This leads to a very efficient procedure for the considered design problem. Computer simulations show that the proposed design technique can achieve better results in fewer iterations than conventional approaches when starting at the same preset initial guess. Moreover, the proposed design technique produces almost the same good results in six iterations if it starts at a better initial guess compared to the preset initial guess. By incorporating the proposed technique with a weighted least squares (WLS) algorithm, we further facilitate the design of QMF banks whose overall reconstruction error is minimized in the minimax sense over the entire frequency band. The WLS algorithm is previously developed by the authors. Computer simulations for illustration and comparison are also provided.