Spline polynomial approach for the design of quadrature mirror filters

This paper presents a design method of the optimum quadrature mirror filters (QMF), by using spline polynomial functions. It is known 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. The solution is to approximate the response of each frequency band by using spline polynomial functions, that insures continuous superior order derivatives. In the proposed approach, the prototype filter is optimized with the novelty of using spline polynomials in the transition band. Several design examples are included to illustrate the proposed algorithm.