Characterization of Matrices Generating Orthogonal Multi-wavelets

Theoretically, multiwavelets hold significant advantages over standard wavelets, particularly for solving more complicated problems, and hence are of great interest. It is pointed out in this paper that we must avoid those "multi-wavelets" being just pairs of standard wavelets. The main purpose of this paper is to charaterize a class of matrices which is crucial for the construction of orthogonal multi-wavelets with uniform linear phase.