On factorization of M-channel paraunitary filterbanks

We systematically investigate the factorization of causal finite impulse re sponse (FIR) paraunitary filterbanks with given filter length. Based on the singular value decomposition of the coefficient matrices of the polyphase representation, a fundamental order-one factorization form is first propose d for general paraunitary systems, Then, we develop a new structure for the design and implementation of paraunitary system based on the decomposition of Hermitian unitary matrices, Within this framework, the linear-phase fil terbank and pairwise mirror-image symmetry filterbank are revisited, Their structures are special cases of the proposed general structures. Compared w ith the existing structures, more efficient ones that only use approximatel y half the number of free parameters are derived. The proposed structures a re complete and minimal. Although the factorization theory with or without constraints is discussed in the framework of nl-channel filterbanks, the re sults can be applied to wavelets and multiwavelet systems and could serve a s a general theory for paraunitary systems.