Orthogonal multiwavelets with dilation factor a

Abstract

There are perfect construction formulas for the orthonormal uniwavelet. However, it seems that there is not such a good formula with similar structure for multiwavelets. Especially, construction of multiwavelets with dilation factor a(a ≥ 2, a ∈ Z) lacks effective methods. In this paper, a procedure for constructing compactly supported orthonormal multiscale functions is first given, and then based on the constructed multiscale functions, we propose a method of constructing multiwavelets, which is similar to that of uniwavelet. Finally, we give a specific example illustrating how to use our method to construct multiwavelets.