Abstract: The notion of vector-valued multiresolution analysis is introduced and the con-cept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and suffcient condition on the existence of orthogonal vector-valued wavelets is given by means of parauni-tary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L²(R,Cⁿ) from these wavelet packets. 

Key words: orthogonal, Hermitian matrix, vector-valued multiresolution analysis, vectorvalued scaling functions, vector-valued wavelets, vector-valued wavelet packets