Sampling errors of correlograms with and without sample mean removal for higher-order complex white noise with arbitrary mean

摘要

We derive the bias, variance, covariance, and mean square error of thestandard lag windowed correlogram estimator both with and without sample meanremoval for complex white noise with an arbitrary mean. We find that thearbitrary mean introduces lag dependent covariance between different lags ofthe correlogram estimates in spite of the lack of covariance in white noise fornon-zeros lags. We provide a heuristic rule for when the sample mean should be,and when it should not be, removed if the true mean is not known. The samplingproperties derived here are useful is assesing the general statisticalperformance of autocovariance and autocorrelation estimators in differentparameter regimes. Alternatively, the sampling properties could be used asbounds on the detection of a weak signal in general white noise.