The third-order cumulant of speech signals with application to reliable pitch estimation

This paper provides a formal framework for using the third-order statistics (TOS) of speech signals and presents a new method for estimating the pitch and making voicing decision using the 3rd-order cumulant of the LPC residual. Analytical expressions for the horizontal slice of the 3rd-order cumulant as well as the kurtosis of voiced speech are derived using the McAulay sinusoidal model (McAulay et al., 1986). The derivations demonstrate that the skewness of voiced speech is sufficiently distinct from that of Gaussian noise and can be used to aid in detecting voicing. It is also shown that the 3rd-order cumulant slice has distinct characteristics in terms of periodicity, phase and harmonic content and is a reliable candidate for estimating the pitch. Actual speech data is used to verify the derivations and experimental results using Gaussian and street noise are used to demonstrate the performance in noisy conditions.