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二阶仿酉矩阵的通解
The general solution to second order paraunitary matrices
【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.
【Abstract】 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;
【Key words】 paraunitary matrix; Cayley transform; orthogonal filter banks;
【Key words】 paraunitary matrix; Cayley transform; orthogonal filter banks;
【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)
- 【文献出处】 安徽大学学报(自然科学版) ,Journal of Anhui University(Natural Science Edition) , 编辑部邮箱 ,2013年05期
- 【分类号】O151.21
- 【下载频次】66