An efficient algorithm to design weighted minimax perfect reconstruction quadrature mirror filter banks

An efficient algorithm is presented to design lattice structure two-channel perfect reconstruction quadrature mirror filter (PR-QMF) banks. We formulate the filter bank design problem as an unconstrained weighted least squares problem with respect to the coefficients of the lattice structure. The proposed iterative algorithm optimizes the lattice coefficients and provides flexible control of the filters' stopband ripple profiles. Typically, only a few iterations of the algorithm are needed to obtain an optimal solution in the weighted minimax sense. We include a set of practical design rules for use with our algorithm. These rules allow very good estimation of important filter bank characteristics, such as the filter length and the number of signed digits for quantization of the lattice coefficients into canonic signed digit representation, to meet a given set of PR-QMF bank specifications.