摘要
一个元素定义在复数域上的罗朗多项式的n×r的矩阵P(z)能被扩充为一个仿酉矩阵 ,当n =2时 ,矩阵的扩充是唯一的 ;当n≥ 3时 ,矩阵的扩充有无穷多种 .因此可用此方法构造出很多种不同的r重紧支撑向量小波和预小波 (n≥3) ,从而也给出了同一尺度函数相对应的紧支撑向量小波或预小波非唯一的构造算法 .
An n×r matrix P(z) , n≤r ,with Laurent polynomial entries in one complex variable z,can be extended to a paraunitary matrix, and when n≥3 paraunitary extending isn't unique.The algorithm can be applied to the construction of compactly supported wavelets and prewavelets from multiresolutions generated by serveral univariate scaling functions with an arbitrary dilation parpmeter.Finally,the corresponding examples are given.
关键词
小波基
预小波
矩阵
扩充
仿酉矩阵
多项式相位矩阵
wavelet bases
prewavelets
matrix extension
paraunitray matrix
polyphase matrix
