Grouped B-spline functions for the design of Quadrature Mirror Filters

The design of two channel Quadrature Mirror Filter (QMF) banks is considered with constraints on the peaks of the reconstruction error and that of the subband filter ripple sizes. In this paper a design method of the optimum quadrature mirror filters (QMF), by using grouped B-spline functions in each transition band, is presented. It was shown that linear phase FIR filters cannot exactly satisfy the condition that the squared amplitude frequency responses are mirror images of each other about the line ω = π / 2, which has led to the name quadrature mirror filters. It is important to have a flat frequency response for the filters. The solution is to approximate the response of each frequency band by using grouped B-spline functions, that insures continuous superior order derivatives.