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Construction of Parseval wavelets from redundant filter systems
Journal article   Peer reviewed

Construction of Parseval wavelets from redundant filter systems

L. W Baggett, P. E.T Jorgensen, K. D Merrill and J. A Packer
Journal of mathematical physics, Vol.46(8), pp.083502-083502-28
2005
DOI: 10.1063/1.1982768
url
https://arxiv.org/pdf/math/0405301View
Open Access

Abstract

We consider wavelets in L 2 ( R d ) which have generalized multiresolutions. This means that the initial resolution subspace V 0 in L 2 ( R d ) is not singly generated. As a result, the representation of the integer lattice Z d restricted to V 0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R d can be constructed directly from the generalized wavelet filters.

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