Global optimization design of QMF filter banks

Abstract

In this paper, we present a new global optimisation method for designing QMF (quadrature mirror filters) filter banks. We formulate the design problem as a nonlinear constrained optimization problem, using the reconstruction error as the objective, and the stopband ripple, stopband energy, pass-band ripple, pass-band energy and transition bandwidth as constraints. This formulation allows us to search for solutions that improves with respect to the objective, and that performs better than or equal to the best existing designs with respect to the constrained measures. We present NOVEL, a global optimisation method we have developed for solving nonlinear continuous constrained optimisation problems, and apply it to find improved designs. We also show that relaxing the constraints on transition bandwidth and stopband energy will lead to significant improvements in the other performance measures.