Optimal cepstrum smoothing

The cepstrum of a random process has proven to be a useful tool in a wide range of applications. The common cepstrum estimator based on the periodogram suffers from large variance, and, to a smaller degree, from bias. The variance can be reduced by smoothing. However, the smoothing may be performed in four different domains: the covariance, the spectral, the log-spectral, and the cepstral domain. We present the mean square error (MSE) optimal smoothing kernels in each domain for estimation of the cepstrum. The lower MSE bound of each of the four families of estimators are compared. We also demonstrate how the four MSE optimal estimators differ in robustness.

► The cepstrum of a random process is a useful tool in many applications.
► Smoothing techniques are often used to reduce the variance of the cepstrum estimate.
► Four different families of smoothed cepstrum estimators can be defined.
► We derive the lower MSE bound of each family and discuss their relation.