Mean-Square Error in Periodogram Approaches with Adaptive Windowing

Modified periodogram approaches are nonparametric power spectral density (PSD) estimators. Here, we present a method for estimating the mean-square error (MSE) of these PSD estimators. The proposed approach uses the observed data to estimate not only the PSD but also the associated MSE simultaneously. The MSE estimate from the Blackman–Tukey approach can be utilized for comparison and choice of the optimum window among a set of smoothing windows of possibly different lengths. For Bartlett and Welch methods, the MSE estimate can be used for quality evaluation, and also enables the use of an additional smooth windowing for these modified periodogram approaches. The optimum adaptive windowing improves the performance of these approaches in the MSE sense. Furthermore, the optimally windowed autocorrelation estimate can be used for extrapolation with the maximum entropy method (MEM). Our simulation results confirm that the proposed optimum smooth windowing approach effectively improves the performance of modified periodogram PSD estimates in the MSE sense.