Construction of Parseval wavelets from redundant filter systems

Details Construction of Parseval wavelets from redundant filter systems Construction of Parseval wavelets from redundant filter systems

2004-05-14

arxiv.org/abs/math/0405301v4

Mathematics

Classical Analysis and ODEs

34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos in Sections 1 and 4, v3 adds a number of references on G

Scientific paper

10.1063/1.1982768

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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