Construction of Parseval wavelets from redundant filter systems

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. (c) 2005 American Institute of Physics.