引进多尺度向量值正交小波与向量值小波包的概念.运用仿酉向量滤波器理论和矩阵理论,给出多尺度向量值正交小波存在的充要条件.提供紧支撑向量值正交的构建算法,给出相应的构建算例.利用时频分析方法与算子理论,刻画一类向量值正交小波包的性质.得到向量值小波包的正交公式.构造向量值函数空间L2 (R,Cn)的规范正交基.%The notion of orthogonal vector-valued wavelets with multiple scale and vector-valued wavelet packets were introduced. A necessary and sufficient condition on the existence of such wavelets was de rived by virtue of the paraunitary vector filter bank theory and matrix theory. A constructive algorithm was provided for the vector with short support. A corresponding constructive example was given. By using time-frequency analysis method and operator theory, the properties of a class of vector-valued orthogonal wavelet packets were characterized and the orthogonality formula was obtained for the wavelet packets. The orthonormal base of vector-valued function space L2(R,C") was constructed.
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