A new approach to nonparametric spectral density estimation

Abstract

A novel approach to nonparametric spectral density estimation has been proposed. The approach is based on a new evaluation criterion called autocorrelation mean square error (AMSE) for power spectral density (PSD) estimates of available finite length data. Minimization of this criterion not only provides the optimum segmentation for existing PSDE approaches , but also provides a new optimum windowing within the segments that can be combined additionally to the existing methods of nonparametric PSDE. Furthermore, the problem of frequency resolution in existing PSDE methods for noisy signals has been analyzed. In the existing approaches, the additive noise and the finiteness of data which are the causes of the original loss of the frequency resolution are not treated separately. The suggested new approach to spectrum estimation takes advantage of these two different causes of the problem and tackles the problem of resolution in two steps. First, the method optimally reduces noise interference with the signal via minimum noiseless description length (MNDL). The new power spectrum estimation MNDL-Periodogram of the denoised signal is then computed via conventional indirect periodogram to improve frequency resolution.