文献类型：期刊文献

中文题名：基于仿酉矩阵的紧支撑二元正交小波滤波器组的构造

英文题名：CONSTRUCTION OF COMPACTLY SUPPORTED BIVARIATE ORTHOGONAL WAVELET FILTER BANKS BASED ON PARAUNITARY MATRICES

作者：李林杉[1,2];彭思龙[3]

第一作者：李林杉

机构：[1]北京联合大学基础部;[2]中科院自动化所,北京100080;[3]中科院自动化所

第一机构：北京联合大学基础教学部

年份：2006

卷号：28

期号：3

起止页码：309-320

中文期刊名：计算数学

外文期刊名：Mathematica Numerica Sinica

收录：CSTPCD;;北大核心:【北大核心2004】；CSCD:【CSCD2011_2012】；

语种：中文

中文关键词：仿酉矩阵;滤波器组;小波

外文关键词：paraunitary matrix, filter banks, wavelet

摘要：高维小波是处理多维信号的有力工具,张量积和栅格结构的小波有其自身的特点,但在实际应用中,我们仍需要构造小波滤波器来满足特定情形下的需要以提高滤波的效果,而构造正交滤波器,在多相域里就等价于构造仿酉阵,在本文中,我们通过对仿酉矩阵的研究,证明二元一次对称的仿酉阵一定能够块对角化,利用这种性质,给出了不可分离的二元正交小波滤波器组及线性相位小波滤波器的构造,并给出了相应的例子．
Mutlivariate wavelets are powerful tool for multidimension signal processing. Wavelets filters constructed by tensor product or lattice structure has their characterization themselves. In application, to improve the effect of filtering, we still need to construct wavelet filter to meet some special requirements. But in the polyphase domain, construction of orthogonal filter banks is equivalent to constructing paraunitary matrices. In this paper, we study paraunitary matrices at first, we prove that symmetric paraunitary matrices with bivariate are able to characterized by block diagonal matrix. Using this property, we construct non-separable bivariate orthogonal wavelet filter banks and also construct filters with linear phase. Some examples are given.