二阶仿酉矩阵的通解  

The general solution to second order paraunitary matrices

作　　者：李林杉[1] 常广平[1] 车燕[1] 

机构地区：[1]北京联合大学基础部,北京100101

出　　处：《安徽大学学报（自然科学版）》2013年第5期1-5,共5页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10972030);北京联合大学新起点计划项目(ZK10201311;ZK10201308)

摘　　要：在多项域里构造正交小波滤波器组等价于构造仿酉矩阵,而仿酉矩阵的构造涉及非线性方程组的求解.通过对Cayley变换的研究,给出构造仿酉矩阵的条件,利用这些条件给出元素为二元一次多项式的二阶仿酉矩阵的通解,并给出了算例.In the polyphase domain, construction of orthogonal filter banks was equivalent to constructing paraunitary matrices , which led to solving sets of nonlinear equations. By the cayley transform of research, we gave the condition of constructing paraunitary matrices at first, then using these conditions, we gave the general solution to second order paraunitary matrices （ each element was a bivariate polynomial of order one） , and some examples were also given.

关 键 词：仿酉矩阵 Cayley变换 正交小波滤波器组 

分 类 号：O224[理学—运筹学与控制论]