COMPARATIVE STUDY OF FRACTAL BEHAVIOR IN QUASI-RANDOM AND QUASI-PERIODIC SPEECH WAVE MAP

Abstract

Fractal behavior in the quasi-steady states of the two types of speech signals, namely, quasi-periodic and quasi-random, are studied. The signals of the first group consist of seven vowels and those for the second group consist of three variants each of three sibilants. Ten rendering of each of these signals by one native Bengali male speaker of 45 years of age are used as the signal database. Standard box-counting method is used for generating ln (pq) versus ln (1/r) curves. D0, Dq and the knee expanse (KE) of the curves, their interrelations and the projections on the source characteristics are the objects of analysis. D2>D0 is found to indicate locally dense nature of the map and are found to be associated mainly with some sibilants. Dq are found to be a family of simple polynomial functions of q for all signals. D0, Dq and KE are related to the nature of different signals and character of the sources generating the signals. The study of fractal dimensions and the generalized dimensions for these signals reveal intermittency behavior and multifractality, which indicate basically, turbulent source or sources for speech generation. That the quasi-periodic and the quasi-random sounds are fundamentally different is reflected in the behavior of generalized fractal dimensions.