Design of FIR Quadrature Mirror-Image Filter Banks Using Fuzzy Adaptive Simulated Annealing

An alternative approach for designing quadrature mirror filter (QMF) banks is presented. Although it is used in this paper to fit filter banks to frequency domain specifications, the method is able to be used in other tasks of digital filter synthesis, when it is possible to convert the original problem into a global minimization one. Here, the overall target is to find adequate coefficients for the prototype filter H₀, so that the filter banks satisfy jointly global performance indices, such as the ripple in the frequency response of the whole system and out of band rejection of the prototype filter. The chosen global optimization algorithm is based upon the well-known simulated annealing paradigm and its implementation known as fuzzy adaptive simulated annealing. The method starts from frequency domain constraints to a generic, parameterized QMF bank family, synthesizes a corresponding real-valued cost function (of prototype filter coefficients) reflecting those constraints and, finally, obtains particular parameter values that determine the proposed optimal system. Besides, it will be presented a multi-objective approach to that classical problem that will make it possible to evaluate tradeoffs involving the complexity of the prototype filter and the reconstruction error produced by the resulting filter bank.