A fast recursive algorithm for system identification and model reduction using rational wavelets

In earlier work by Pati and Krishnaprasad (1992) it was shown that rational wavelet frame decompositions of the Hardy space H²(II⁺) may be used to efficiently capture time-frequency localized behavior of stable linear systems, for purposes of system identification and model-reduction. In this paper we examine the problem of efficient computation of low-order rational wavelet approximations of stable linear systems. We describe a variant of the matching pursuit algorithm of Mallat and Zhang (1992) that utilizes successive projections onto two-dimensional subspaces to construct rational wavelet approximants. The methods described here are illustrated by means of both simulations and experimental results