The Characterization of a Class of Orthogonal Multiple Vector-valued Compactly Supported Wavelet Packets with Five-scale

Since 1986, Wavelet analysis has become a popular subject in scientific research. It has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. In this article, the multiple vector-valued wavelet packets are defined and investigated. A procedure for constructing the multiple vector-valued wavelet packets is presented. The properties of multiple vector-valued wavelet packets are discussed by using integral transformation and operator theory. Finally, new orthogonal bases of L²(R, C^{u times u}) is constructed from the orthogonal multiple vector-valued wavelet packets.