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.

翻译：从采样且时间有限的信号中推导自协方差函数，或从两个此类信号中推导互协方差函数时，需对信号进行均值估计并去除均值。若无法预先获知正确的均值信息，且必须从时间序列本身推导均值，则估计结果将存在偏差。针对独立数据方差估计的校正方法——贝塞尔校正已广为人知。本文展示了针对自协方差与互协方差函数的类似校正方法，包括对样本进行单独加权。在校正后的估计量基础上，还可进一步纠正相关数据场景下方差估计的偏差。本文所用程序可通过http://sigproc.nambis.de/programs在线获取。