Design of symmetric bi-orthogonal double density wavelet filter banks

Abstract

We look at the design of a class of oversampled filter banks and the resulting framelets. The oversampled property is achieved via an extra subband resulting in double density filter banks (DDFB's). We design a class of such filters with linear phase property. We look at a special class of framelets from a filter bank perspective, in that we design double density filter banks (DDFB's). We define type 1 polyphase representation as X (z) = /spl Sigma//sub k=0//sup 1/ z/sup -k/X/sub k/(z/sup 2/) and type 2 polyphase representation as X (z) = /spl Sigma//sub k=0//sup 1/ z/sup k/X/sub k/(z/sup 2/). Polyphase matrices are given in the article, where H/spl tilde/(z) is the type 1 analysis polyphase matrix, and H(z) is the type 2 synthesis polyphase matrix, we can write the perfect reconstruction condition as [H(z)]/sup T/ H/spl tilde/(z) = I.