Multiscale statistical signal processing

A novel framework for multiscale statistical signal processing is introduced. Its purpose is to provide a statistical toolbox to analyze properties of signals involving time and scale simultaneously. Stationary processes over the dyadic tree are borrowed from harmonic analysts for this purpose, and a new partial order is proposed to model causality in scale. Autoregressive processes are investigated, and it is shown that Schur-Levinson parameterizations play a crucial role. As expected from the model, the restriction at a given scale (level) of a sample of such processes looks like a fractal, i.e. a random signal appearing similar whether seen from close or far away