A nonlinear dynamical systems analysis of fricative consonants

Abstract

Acoustic waveforms of the strident fricatives /s/, /z/, /integral of/, and /3/ spoken by two native American English speakers are analyzed using modern chaotic analysis techniques. Fricative data are extracted from both intervocalic and sustained utterances. For comparison, acoustic waveforms of the vowels /a/, /i/, and /u/ are also analyzed. For 44% of the unvoiced fricative tokens in VCV contexts and 59% of the sustained voiced fricatives, indications of low-dimensional dynamics could be found with the given limitations of stationarity. The low-dimensional chaotic behavior is exhibited by a correlation dimension (D2) ranging between 3 and 7.2, and by positive maximum Lyapunov exponents (LEs). For the remaining fricatives, results suggest that the dimensional complexity therein is greater than the maximum D2 value that could be reliably estimated from the available data (about 7.8 for the intervocalic cases and 9 for the sustained cases). Intervocalic voiced fricatives are excluded from the analysis due to stationarity requirements. Analysis of vowels, on the other hand, indicates nonchaotic behavior demonstrated by folded limit cycles and nonpositive maximum LEs; this is consistent with results of previous studies. Findings are interpreted in terms of posited articulatory and aerodynamic parameters of turbulence in the production of fricative consonants.