Fourth Moment and Its Functional Transformations as Measures of Clipping Degree and Quality of Acoustic Signal

It is shown that fourth standardized moment (kurtosis) and its some functional transformations (inverse value, square root of inverse value) can be objective measures of clipping and quality of speech and music signals. The essential advantages of suggested measures are no need for previous estimation of probability density of analyzed signal as well as no need for information about undistorted signals. Indices of correlation were calculated and correspondence maps were created that represent relationships between estimations of suggested measures and subjective quality evaluations of clipped sound signals, which enables calibration of objective measures. It was shown that values correspondence maps, which are simple functional transformations of kurtosis, can be approximated by polynomials of the first or second order, whereas for the approximation of correspondence maps of kurtosis the polynomials of the fourth order are needed. This fact in combination with interval limitations of possible values of used measures means that in engineering applications the applying of kurtosis functional transformation can be preferable. Suggested measures were compared to different measures represented by clipping factor. The clipping factor was shown to be less effective compared to suggested measures under conditions of high clipping level of speech and music signals.