BALANCED MULTIWAVELETS ON THE INTERVAL [0, 1] WITH ARBITRARY INTEGER DILATION FACTOR a

摘要

In this paper, orthogonal multiwavelets on interval [0, 1] with arbitrary compact support γ and integer dilation factor a are studied. Firstly, the concept of multiwavelets on the interval [0, 1] is generalized to the arbitrary integer dilation factor a, a ≥ 2, a ∈ Z, and an algorithm for constructing orthogonal multiscaling function and multiwavelets on interval [0, 1] with dilation factor a is presented. Secondly, the decomposition and reconstruction formulas of multiwavelets on interval [0, 1] are deduced. Finally, the "balancing" concept of multiwavelets on the interval [0, 1] with dilation factor a is defined, and the algorithm of balancing the unbalanced multiwavelets on the interval [0, 1] is also given.