Wavelets with the Translation Invariance Property of Order N

Abstract

All wavelets can be associated to a multiresolution like structure, i.e. an incr easing sequence of subspaces of L^2(R). We consider the interaction of a wavel et and the translation operator in terms of which of the subspaces in this multi resolution like structure are invariant under the translation operator. This ac tion defines the notion of the translation invariance property of order n. In this paper we show that wavelets of all levels of translation invariance exist, first for the classic case of dilation by 2, and then for arbitrary integral di lation factors.