Easy-to-compute parameterizations of all wavelet filters: input-output and state-space
Abstract
We here use notions from the theory linear shift-invariant dynamical systems to provide an easy-to-compute characterization of all rational wavelet filters. For a given N bigger or equql to 2, the number of inputs, the construction is based on a factorization to an elementary wavelet filter along with of m elementary unitary matrices. We shall call this m the index of the filter. It turns out that the resulting wavelet filter is of McMillan degree $N((N-1)/2+m). Rational wavelet filters bounded at infinity, admit state space realization. The above input-output parameterization is exploited for a step-by-step construction (where in each the index m is increased by one) of state space model of wavelet filters.
Keywords
Cite
@article{arxiv.1105.0256,
title = {Easy-to-compute parameterizations of all wavelet filters: input-output and state-space},
author = {Daniel Alpay and Palle Jorgensen and Izchak Lewkowicz},
journal= {arXiv preprint arXiv:1105.0256},
year = {2013}
}
Comments
The present version is better coordinated with another work of us on the same subject, entitled Extending wavelet filters. Infinite dimensions, the non-rational case and indefinite-inner product spaces, and also available on arxiv at: http://arxiv.org/abs/1106.2303