Investigations of errors in sample autocovariance functions and their corresponding power spectra

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Abstract
This paper concerns the calculation of autocovariance (autocorrelation) functions and the corresponding power spectra from a set of finite samples selected from the infinite population. In many optical experiments involving statistical fluctuations we wish to subtract the population mean from each measurement when the population mean is unknown. It is shown that subtracting the sample mean from each sample measurement leads to definite and predictable errors in the autocovariance function and its corresponding power spectrum. We show in a computer-generated example that the error introduced has significance in the autocovariance function but has much less significance in the power spectrum.