BALANCED INTERPOLATORY MULTIWAVELETS WITH MULTIPLICITY r

Abstract

Vector-valued refinable interpolatory functions with multiplicity r are discussed in this paper. This kind of refinable functions have a sampling property like Shannon's sampling theorem, and corresponding matrix-valued refinable masks possess special structure. In the context of multiwavelets, some properties of multifilter banks related will be present. Based on these properties, it will be shown that there are no symmetric (or antisymmetric) vector-valued refinable functions with interpolatory property. In the practical application, multiwavelets are always required to possess a certain degree of smoothness, which is related to three different concepts: balancing order, approximation order and analysis-ready order. In the general case, three notions are different. But if the scaling function is interpolatory, three concepts will be verified to equal to each other. Finally, a complete characterization of multifilter banks {H, G} will also be given and it will be used to construct some new balanced multiwavelets with interpolatory property for case r = 2, corresponding to which, multifilter banks have rational coefficients.