An Algorithm for Designing Vector-Valued Wavelets and the Presentation of Vector-Valued Wavelet Packet Bases

In this paper, we introduce orthogonal vector-valued wavelets with 3-scale. We propose a necessary and sufficient condition for the existence of orthogonal vector-valued wavelets by using paraunitary vector filter bank theory, we develop a new procedure for constructing a class of orthogonal compactly supported vector-valued wavelets. Characterization of vector-valued wavelet packets is investigated by virtue of time-frequency method and algebra theory. Moreover, it is shown how to construct various orthonormal bases of a vector-valued function space from these wavelet packets.