Design of perfect reconstruction filter banks using transformation of variables and re-factorization

In this paper we present a technique to design 2-channel perfect reconstruction filter banks by using a combination of transformation of variables and re-factorization. The transformation of variables technique was initially formulated for the design of M-D (multidimensional) filter banks. With this technique the factorization of M-D polynomials (product filter) is avoided and high quality linear phase filters with sharp frequency roll-off can be designed with ease. Although the factorization problem does not occur in the 1-D case the technique is still effective for designing 1-D filter banks as it provides the flexibility of controlling the frequency characteristics of the filters with ease. The filters obtained using this technique always have an odd number of coefficients. By using re-factorization we are able to improve the quality of the filters and also obtain filters with an even number of coefficients.