Spectrogram Smoothing for Estimation of the Evolutionary Spectra of Uniformly Modulated Processes

Among nonstationary time series, the class of Uniformly Modulated Processes (UMPs) have Evolutionary Power Spectra (EPS) that are the outer product of a modulating time-function and the spectrum of a stationary process. In this paper, we propose a smoothing procedure on an estimator of the EPS of a general nonstationary process to obtain an estimator of the EPS of a UMP. This is done by obtaining isolated estimates of the time-modulating function and the spectrum of the stationary component of a UMP, and then combining them to form our smoothed EPS estimate. Via simulation, we compare our estimator to the High Resolution Spectrogram and an estimator minimizing the Frobenius norm between the general estimator and one with the structure of a UMP’s EPS.