Signal modeling using increments of extended self-similar processes

Abstract

The article expands the fractional Brownian motion (fBm) model by investigating the idea of generalizing self-similarity to create extended self-similar (ESS) processes for which fBm processes are a subset. Properties of ESS processes are discussed, and an ESS increment model parameterized by variables controlling short and long term correlation effects is examined. We propose a fast parameter estimation algorithm for the new model which is based on the decorrelation effect of the Haar transform on the ESS increments, and we demonstrate the performance of this parameter estimation algorithm with numerical simulations.<>