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An Investigation into Vector-valued Multivariate Wavelet Packets

Wavelet analysis has become a popular subject in scientific research for twenty years. In this paper, the notion of orthogonal vector-valued multivariate wavelet packets with four-scale is introduced. A method for constructing them is presented. Their orthogonal property is characterized by virtue of finite group theory, time-frequency analysis method and matrix theory. Three orthogonality formulas are established.