Singularity processing of nonstationary signals

Abstract

This paper presents a new approach in processing nonstationary signals-such as speech signals and images-through singularity characterization. In this approach, we associate a singular measure /spl mu//sub f(t/) (r) with a transient at time t of a signal f(t) (where a real number r>0 is a time perturbation around t) and use the singularity behaviour of the measure for the characterization of the signal nonstationarity. The approach is capable of characterizing isolated transients through Holder exponents (or singularity strength), as well as mixture transients (e.g. singularity everywhere) through the concept of fractality and multifractality. The paper discusses the concept and the practicality of applying this approach to signals. The paper also shows that this approach can provide a unifying framework for previously published work on applying nonlinear, chaotic, fractal, and multifractal analysis to signals. We show that the main conceptual issue in applying fractality and multifractality to signals using this framework is the proper selection of signal measures.