Pade table, continued fraction expansion, and perfect reconstruction filter banks

We investigate the relationships among the Pade table, continued fraction expansions and perfect reconstruction (PR) filter banks. We show how the Pade table can be utilized to develop a new lattice structure for general two-channel bi-orthogonal perfect reconstruction (PR) filter banks. This is achieved through characterization of all two-channel biorthogonal PR filter banks. The parameterization found using this method is unique for each filter bank. Similar to any other lattice structure, the PR property is achieved structurally and the quantization of the parameters of the lattice does not effect this property. Furthermore, we demonstrate that for a given filter, the set of all complementary filters can be uniquely specified by two parameters, namely, the end-to-end delay of the system and a scalar quantity. Finally, we investigate the convergence of the successive filters found through the proposed lattice structure and develop a sufficient condition for this convergence