Optimized weighted averaging of peak matched multiple window spectrum estimators

Periodogram averaging with multiple windows can be used in spectrum analysis of nonstationary data. Usually, however, the windows for the subspectra are equally weighted in the estimate. In this correspondence, a criterion for the optimization of weighting factors is formulated as the average of normalized bias, variance, or mean square error in a certain frequency interval around a predefined peaked spectrum. The weighting factors are optimized using the peak matched multiple windows, the sinusoid multiple windows, and the discrete prolate spheroidal sequences.