Parametrization of discrete finite biorthogonal wavelets with linear phase

We present a parametrization of discrete finite biorthogonal wavelets with linear phase. Our approach is similar to Zou and Tewfik's (see IEEE Transaction on Signal Processing, vol.41, no.3, p.1428-31, 1993) for orthogonal wavelets in the way that we utilize a lattice factorization of polyphase matrices of two-channel PR filter banks. However in the biorthogonal case we are faced with the additional possibility of having length differences between the low- and high-pass filters. Our solution to this problem is the introduction of a set of initial polyphase matrices for the lattice product in order to provide the possibility of choosing a certain length difference between the two corresponding filters. This modification of the original lattice product enables us to generate a larger class of discrete wavelets in a systematic way.