Design of filter banks using transformation of variables: new results

Abstract

The design problem of multirate filter banks can be divided into two parts. The first part involves the issue of reconstruction errors. The second part involves the issue of designing good quality subband filters. There is a class of techniques that we refer to as transformation of variables which satisfactorily addresses the two parts of the design problem. This class of filter banks is specified by its prototype filters and transformation (kernel). It is the flexibility and relative ease in designing the kernel that enables the technique to satisfactorily address the second part of the design problem. We present two new methods of designing the kernel that will enhance the design techniques' flexibility and effectiveness. The first is the combination of the McClellan transformation and rotation operators. The second introduces and uses the concept of directional singular value decomposition (SVD).