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To derive the auto-covariance function from a sampled and time-limited signalor the cross-covariance function from two such signals, the mean values must beestimated and removed from the signals. If no a priori information about thecorrect mean values is available and the mean values must be derived from thetime series themselves, the estimates will be biased. For the estimation of thevariance from independent data the appropriate correction is widely known asBessel's correction. Similar corrections for the auto-covariance and for thecross-covariance functions are shown here, including individual weighting ofthe samples. The corrected estimates then can be used to correct also thevariance estimate in the case of correlated data. The programs used here areavailable online at http://sigproc.nambis.de/programs.

Practical Realization of Bessel's Correction for a Bias-Free Estimation of the Auto-Covariance and the Cross-Covariance Functions