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

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