Nonlinearity in Speech Signal

Abstract

Nature abounds in nonlinearity. The human vocal tract system exhibits a nonlinear dynamical behavior that creates turbulence during production of speech signals, even during the utterance of vowels. In view of this, it is imperative to determine whether the dynamics can be described as a low-dimensional chaotic system with a tractable number of degrees of freedom. Vortices in the airflow have been experimentally found above the glottis. In a deterministic model, a large number of active degrees of freedom with stochastic models would be required to characterize this irregular vibratory behavior. Theory of chaos seems to help us here. Generally, the nature of chaotic behavior is studied by viewing the relationship of the curve representing this tent-like data distribution with the identity line. It is possible to determine the behavior of the orbits of maps from the cobweb plots. In the case when the orbit is periodic, it is also possible to identify the period of an orbit from the plot, i.e., the minimum number of iterates required orbit to return to the same points. Chaotic orbits (with infinite periodicity but limited in a certain zone) were also observed in several cases. In certain limited cases, unstable orbits are observed for all choices of initial conditions and the result of five utterances of vowel /Ɔ/ and /ɐ/ of two speakers shows different types of orbits. In all these cases, particularly those which produce stable points, periodic points or chaotic orbits, the orbits have been studied for different initial points but within the limits stated, the final sets obtained remain the same.