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Construction of Parseval wavelets from redundant filter systems

L. W. Baggett·P. E. T. Jorgensen·K. D. Merrill·J. A. Packer
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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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BibTeXRIS

L. W. Baggett, P. E. T. Jorgensen, K. D. Merrill, J. A. Packer. 2005-05-05. Construction of Parseval wavelets from redundant filter systems. https://doi.org/10.1063/1.1982768

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