Hidden frequency estimation with data tapers (Q2703250)

The authors consider data of the form \(s(n)=\sum_{k=1}^K 2A_k\cos(\omega_k n+\varphi_k)+x(n)\), where \(A_k\), \(\omega_k\), \(\varphi_k\) are unknown parameters, and \(x(n)\) is a stationary linear process with unknown spectral density. The problem is to estimate the ``hidden frequencies'' \(\omega_k\). The authors describe two methods (maximum of periodogram and secondary analysis) where they propose to use data tapering. It is shown that the obtained estimators are asymptotically normal with limit variance worse than for estimators without tapering. But it is demonstrated that tapering improves the bias of the estimators. Examples are presented in which estimates without tapering are impossible. Simulation results are presented.