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