A. Benveniste et al., MULTISCALE SYSTEM-THEORY, IEEE transactions on circuits and systems. 1, Fundamental theory andapplications, 41(1), 1994, pp. 2-15
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.