Lattice factorization based causal symmetric paraunitary matrix extension and construction of symmetric orthogonal multiwavelets

Abstract

In this paper, we propose a lattice factorization based symmetric paraunitary matrix extension method to design a causal symmetric paraunitary multifilter banks(PUMFBs) and construct compactly supported symmetric orthogonal multiwavelets by using the method.First, we transform a Laurent polynomial matrix consisting of polyphase components of a given symmetric orthogonal multifilter into a Laurent polynomial matrix with a simple structure, and then obtain a lattice factorization based symmetric paraunitary extension matrix by factorizing the transformed Laurent polynomial matrix and extending the constant matrix of the factorization. We also construct symmetric orthogonal multiwavelets by the proposed symmetric paraunitary matrix extension method. Finally, some examples are given to illustrate the proposed symmetric paraunitary matrix extension method.