The research of orthogonal vector-valued wavelet packets

Wavelet analysis has been developing a branch of mathematics. In this paper, the notion of vector-valued univariate wavelet packets is introduced. A new procedure for constructing the vector-valued wavelet packets is presented. Their properties are discussed by virtue of time-frequency analysis method and operator theory. Orthogonality formulas are established. Finally, two new orthogonal bases of L
²
(R,C
ⁿ
) are constructed from these orthogonal multiple vector-valued wavelet packets.