A New Look at Frequency Resolution in Power Spectral Density Estimation

Abstract

The problem of frequency resolution in non-parametric power spectrum density estimation (PSDE) for noisy signals is considered. In this setting, finite length of data as well as the additive noise, both contribute to a decreased frequency resolution. The existing PSDE approaches offer different forms of averaging and windowing of the available data only to improve statistical properties of the estimates, however, at the expense of reducing frequency resolution. In these 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. In this paper, we suggest a new approach which takes advantages of these two different causes of the problem. Therefore, the new nonparametric approach to spectrum estimation 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 (PMNDL) of the denoised signal is then computed via conventional indirect periodogram to improve frequency resolution