Nonlinear dynamical analysis of speech

This paper reports results of the estimation of dynamical invariants, namely Lyapunov exponents, dimension, and metric entropy for speech signals. Two optimality criteria from dynamical systems literature, namely singular value decomposition method and the redundancy method, are used to reconstruct state space trajectories of speech and make observations. The positive values of the largest Lyapunov exponent of speech signals in the form of phoneme articulations show the average exponential divergence of nearby trajectories in the reconstructed state space. The dimension of a time series is a measure of its complexity and gives bounds on the number of state space variables needed to model it. It is found that most speech signals in the form of phoneme articulations are low dimensional. For comparison, a statistical model of a speech time series is also used to estimate the correlation dimension. The second-order dynamical entropy (which is a lower bound of metric entropy) of speech time series is found to be positive. This independently corroborates the interpretation of the largest Lyapunov exponent results and gives an estimate of the predictability time. (C) 1996 Acoustical Society of America.