Lattice Structure for Generalized-Support Multidimensional Linear Phase Perfect Reconstruction Filter Bank
Lattice Structure for Generalized-Support Multidimensional Linear Phase Perfect Reconstruction Filter Bank
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DOI：
10.1109/tip.2013.2279310
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发表时间：
2013-12
影响因子：
10.6
通讯作者：
Xieping Gao;Bodong Li;F. Xiao
中科院分区：
文献类型：
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作者：
Xieping Gao;Bodong Li;F. Xiao
多维线性相位完全重构滤波器组(MDLPPRFB)可以通过格型结构来设计和实现。村松等人提出了具有滤波器组支撑N(MΞ)的MDLPPRFB的格子结构，其中M是抽取矩阵，Ξ是正整数对角线矩阵，N(N)表示矩阵N的基本平行六面体中的整数向量集合。显然，如果Ξ被选为其他正对角线矩阵而不仅仅是正整数矩阵，相应的格子结构将提供更多的滤波器组选择，从而在滤波器组和滤波器组之间提供更好的折衷。我们将这种结果滤波器组称为广义支持MDLPPRFB(GSMDLPPRFB)。然而，GSMDLPPRFB的晶格结构不能通过简单地推广村松使用的过程来设计。此外，辅助设计的相关理论也变得不同于村松使用的理论。这些问题将在本文中加以论述。为了指导GSMDLPPRFB的设计，给出了广义支撑多维滤波器组为线性相位的充要条件。为了确定可以找到GSMDLPPRFB的情况，提出了GSMDLPPRFB存在的必要条件与滤子支持度和对称极性(即对称滤子的个数ns和反对称滤子NA的个数)有关。基于一个过程(与村松使用的不同)，结合多个多相矩阵来构造格子结构的核心构建块之一的开始块，发展了GSMDLPPRFB的格子结构，并证明了该格子结构是最小的。此外，本文的结果还包括村松的特例。
Multidimensional linear phase perfect reconstruction filter bank (MDLPPRFB) can be designed and implemented via lattice structure. The lattice structure for the MDLPPRFB with filter support N(MΞ) has been published by Muramatsu , where M is the decimation matrix, Ξ is a positive integer diagonal matrix, and N(N) denotes the set of integer vectors in the fundamental parallelepiped of the matrix N. Obviously, if Ξ is chosen to be other positive diagonal matrices instead of only positive integer ones, the corresponding lattice structure would provide more choices of filter banks, offering better trade-off between filter support and filter performance. We call such resulted filter bank as generalized-support MDLPPRFB (GSMDLPPRFB). The lattice structure for GSMDLPPRFB, however, cannot be designed by simply generalizing the process that Muramatsu employed. Furthermore, the related theories to assist the design also become different from those used by Muramatsu . Such issues will be addressed in this paper. To guide the design of GSMDLPPRFB, the necessary and sufficient conditions are established for a generalized-support multidimensional filter bank to be linear-phase. To determine the cases we can find a GSMDLPPRFB, the necessary conditions about the existence of it are proposed to be related with filter support and symmetry polarity (i.e., the number of symmetric filters ns and antisymmetric filters na). Based on a process (different from the one Muramatsu used) that combines several polyphase matrices to construct the starting block, one of the core building blocks of lattice structure, the lattice structure for GSMDLPPRFB is developed and shown to be minimal. Additionally, the result in this paper includes Muramatsu's as a special case.