Design of quadrature mirror filters with linear phase in the frequency domain

The design of quadrature mirror filter (QMF) banks whose analysis and synthesis filters have linear phase is considered. Because the design problem in the frequency domain is a highly nonlinear optimization problem, a linearization technique is proposed. An analytical solution formula is obtained, leading to a very efficient procedure. Computer simulations show that the design technique achieves better results in fewer iterations than conventional approaches when starting at the same preset initial guess. Moreover, the 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 technique with a weighted least squares, (WLS) algorithm, the design of QMF banks whose overall reconstruction error is minimized in the minimax sense over the entire frequency band is facilitated. Computer simulations for illustration and comparison are provided