Design of QMF banks based on derivative information

Abstract

New L2 objective functions for the design of quadrature mirror filter (QMF) banks are proposed. They are based on the derivative information of the reconstruction error. Simple and explicit matrix-form formulas for the proposed objective functions are derived. Efficient design methods are proposed by incorporating a separability technique into the derived optimality conditions on prototype filters. The proposed design methods need only solve linear equation iteratively without nonlinear optimisation. Design examples demonstrate that good low-delay QMF banks and linear-phase QMF banks can be obtained in only a few iterations. Compared with the conventional approach, the new approach leads to QMF banks with larger stopband attenuation and smaller reconstruction errors.