B-spline approach for the design of quadrature mirror filters

In this paper a design method of the optimum quadrature mirror filters (QMF), by using symmetric B-spline functions, 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 flters. 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 B-spline functions, that insures continuous superior order derivatives. In the proposed method, the prototype filter is optimized with the novelty of using spline functions in the transition band.