Direct design of orthogonal filter banks and wavelets

This paper presents a new method for the design of two-channel conjugate quadrature (CQ) filter banks in which halfband filter and spectrum factorization are not required. Instead, a CQ filter is directly optimized subject to the perfect reconstruction and possibly other constraints (such as number of vanishing moments (VM)). We develop a design strategy in that the solution is approached sequentially with each update confined to within a small vicinity of the current iterate where the problem at hand behaves like a convex one, thus the update can be obtained as a solution of a convex problem. Four design scenarios are considered, namely the least squares designs with or without VM requirement, and equiripple designs with or without VM requirement. The simulation studies demonstrate that the proposed method is reliable to design high-order CQ filters with improved performance.