Efficient algorithm to design perfect reconstruction regular quadrature mirror filters using weighted Lp error criteria

Abstract

An efficient iterative algorithm is presented in this paper to design lattice-type perfect reconstruction regular quadrature mirror filters (PR-QMF) by minimizing the pth power of an appropriate error criteria, where p can be a function of ω. The filter bank design is approximated as an unconstrained weighted least squares problem with respect to the lattice coefficients. Typically, only a few iterations of our algorithm is needed to obtain an optimal solution in the weighted Lp sense. An estimation of the number of canonic signed digit(CSD) terms needed to quantize the lattice coefficients yielding minimal degradation of the filter's stopband attenuation is also derived. Efficient multiplierless implementation of lattice-type regular PR-QMF banks are easily obtained using this result.