2023/03/20 by Holger Nobach, Nobach, Holger · 1 citation
Decision Sciences · Engineering · Mathematics · #62M10 #FOS: Computer and information sciences #FOS: Electrical engineering #Fault Detection and Control Systems #G.3 #Methodology (stat.ME) #Scientific Measurement and Uncertainty Evaluation #Signal Processing (eess.SP) #Statistical and numerical algorithms #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2303.11047
openalex publication_date 2023/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.