A rational subdivision scheme using cosine-modulated wavelets

Abstract

This paper proposes a rational subdivision scheme using cosine-modulated wavelets. Subdivision schemes constructed from iterated filter banks can be used to generate wavelets and limit functions for multiresolution analysis. The proposed subdivision scheme is based on a kind of nonuniform filter banks called recombination nonuniform filter banks (RN FB). It is shown that if the component FBs in a RNFB are wavelet FBs, then the necessary condition for convergence to limit functions in the subdivision scheme is also satisfied. Therefore, the design of different rational subdivision schemes is considerably simplified. An efficient RNFB, called RN cosine modulated FBs (CMFB), constructed from uniform CMFBs and cosine-modulated transmultiplexers (TMUX) are further investigated. Using a design technique for designing RN CMFB and cosine modulated wavelets (CMW) previously reported by the authors, very smooth limit functions can be generated from the rational subdivision scheme. A design example is given to illustrate the proposed method.