Optimal cepstrum smoothing

Authors:
Johan Sandberg;Maria Hansson-Sandsten
Affiliations:
Lund University, Centre for Mathematical Sciences, Mathematical Statistics, Box 118, SE-221 00 Lund, Sweden;Lund University, Centre for Mathematical Sciences, Mathematical Statistics, Box 118, SE-221 00 Lund, Sweden
Venue:
Signal Processing
Year:
2012

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Abstract

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.