Invariant Measures Based on the U-Correlation Integral: An Application to the Study of Human Voice

Abstract

Nonlinear measures such as the correlation dimension, the correlation entropy, and the noise level were used in this article to characterize normal and pathological voices. These invariants were estimated through an automated algorithm based on the recently proposed U-correlation integral. Our results show that the voice dynamics have a low dimension. The value of correlation dimension is greater for pathological voices than for normal ones. Furthermore, its value also increases along with the type of the voice. The low correlation entropy values obtained for normal and pathological type 1 and type 2 voices suggest that their dynamics are nearly periodic. Regarding the noise level, in the context of voice signals, it can be interpreted as the power of an additive stochastic perturbation intrinsic to the voice production system. Our estimations suggest that the noise level is greater for pathological voices than for normal ones. Moreover, it increases along with the type of voice, being the highest for type 4 voices. From these results, we can conclude that the voice production dynamical system is more complex in the presence of a pathology. In addition, the presence of the inherent stochastic perturbation strengthens along with the voice type. Finally, based on our results, we propose that the noise level can be used to quantitatively differentiate between type 3 and type 4 voices.