An Analysis of Quefrency Selective Temporal Smoothing of the Cepstrum in Speech Enhancement

Smoothing selected cepstral coefficients over time has been recently shown to be a powerful method in the enhancement of noisy speech signals. A difficulty that arises in this context is that averaging a random variable in the log-domain changes its mean in the linear domain. The knowledge of this bias is indispensable for most temporal cepstrum smoothing applications. To date, the bias is known only for Gaussian distributed signals and infinite averaging length. This contribution presents an analytic solution for signals that are recursively smoothed in the cepstral domain with arbitrary effective averaging lengths. Additionally, the correct bias is computed also for a quefrency dependent setting of the recursive averaging parameters.