Kurtosis and Its Transformations as Objective Measures of Clipping Value and Speech Quality

In this paper, it is shown that kurtosis and some of its functional transformations are expedient to use as a measures of the clipping value of speech signals. In addition to the kurtosis, two more measures of the clipping value are considered: they are the reciprocal of the kurtosis, as well as the square root of the reciprocal of the kurtosis. The use of the proposed measures makes it possible to significantly simplify and speed up the calculations in comparison with the methods where it is necessary to preliminarily estimate the probability density function of the analyzed speech signal. It is shown also that the matching maps between the proposed objective measures and the subjective estimates of the speech signals quality are well approximated by a linear function or polynomials of the second and fourth orders. This fact indicates the possibility of building economical, from a computational point of view, algorithms for the control of speech signals quality.