A New Global-Search Method for Designing Filter Banks

In this paper, we present a new global-search method for designing QMF (quadrature-mirrorlter) lter banks. We formulate the design problem as a nonlinear constrained optimization problem, using the reconstruction error as the objective, and the other performance metrics as constraints. This formulation allows us to search for designs that improve over the best existing designs. Due to the nonlinear nature of the performance metrics, the design problem is a nonlinear constrained optimization problem with many local minima. We propose to solve this design problem use global-search methods based on Lagrangian formulations. After transforming the original constrained optimization problem into an unconstrained form using Lagrange multipliers, we apply a new global-search method to nd good solutions. The method consists of a coarse-level global-search phase, a ne-level global-search phase, and a local search phase, and is suitable for parallel computation due to the minimal dependency between various key components. In our experiments, we show that our method nds better designs than existing global-search methods, including simulated annealing and genetic algorithms.