MULTISCALE SYSTEM-THEORY

In many applications it is of interest to analyze and recognize phenom ena occurring at different scales. The recently introduced wavelet tra nsforms provide a time-and-scale decomposition of signals that offers the possibility of such an analysis. Until recently, however, there ha s been no corresponding statistical framework to support the developme nt of optimal, multiscale statistical signal processing algorithms. A recent work of some of the present authors and co-authors proposed suc h a framework via models of ''stochastic fractals'' on the dyadic tree . In this paper we investigate some of the fundamental issues that are relevant to system theories on the dyadic tree, both for systems and signals.