This paper presents a new time-domain-based factorization algorithm for perfect-reconstruction filter bank. In the proposed algorithm, the polyphase transfer matrix is decomposed into elementary blocks using LU representation which can also be implemented by ladder structure. Consequently, perfect reconstruction is structurally imposed and the resulting system is robust to coefficient quantization. We presented an iterative design procedure to obtain perfect reconstruction filter bank with different desired specification on each subband filters. Given several subband filters, a block LU factorization algorithm is presented for perfect reconstruction filter bank completion. Special properties such as linear phase and FIR solution are discussed and parameterization of paraunitary completion under block LU factorization is derived. Block ladder structure are presented for efficient implementation. The proposed structure can be used to design perfect reconstruction filter bank with higher dimension. An example in mapping of 1D perfect reconstruction filter bank with LU representation into 2D perfect reconstruction filter bank with diamond shaped passband using nonrectangular transform is discussed.
C. W. Kok,
Truong Q. Nguyen,
"LU factorization of perfect-reconstruction filter bank", Proc. SPIE 3078, Wavelet Applications IV, (3 April 1997); doi: 10.1117/12.271728; https://doi.org/10.1117/12.271728