Lattice factorization based symmetric PMI paraunitary matrix extension and construction of symmetric orthogonal wavelets

In this paper, we propose a lattice factorization based matrix extension method for constructing the causal FIR symmetric paraunitary filter banks (PUFBs) whose filters H-k (z) , k = 0, 1, ... , M - 1 satisfy the pairwise mirror image (PMI) property, i.e. the condition H-k (z) = HM-1-k (-z) , k = 0, 1, ... , M - 1. And, based on the extension method, we provide a method for constructing compactly supported symmetric orthog-onal wavelets. Firstly, for a given symmetric real-valued M-orthogonal filter H0(z), we propose an algorithm for factorizing a Laurent polynomial matrix composed of polyphase components of the filter pair {H0(z), H0(-z)} into the product of lattice factors and constant matrix. Secondly, based on the lattice factorization algorithm, we propose a method for the causal symmetric PU extension with PMI property of the given Laurent polynomial matrix. This method provides a lattice structure for fast implementation of the resulting symmetric PMI PUFB. Thirdly, we provide a method for constructing compactly supported symmetric orthogonal wavelets by the causal symmetric PMI PU extension. Lastly, several examples are provided to illustrate the construction method proposed in this paper. (c) 2022 Elsevier B.V. All rights reserved.