A multiple window method for estimation of peaked spectra

A multiple window method for estimation of a peaked power density spectrum is designed. The method optimizes a filter function utilizing the Karhunen–Loève basis functions of a known peaked spectrum as windows to reduce variance and bias in the locality of the frequency peak. For improving performance, a penalty function is used to suppress the sidelobes outside a given bandwidth. The improved windows are obtained as the solution of a generalized eigenvalue problem. The bias at the frequency peak is reduced due to matching windows, while the variance is decreased by averaging uncorrelated periodograms. The method is compared with the Thomson multiple window estimator as well as to a single Hanning window in a simulation.