Abstract
A practical method of power spectral estimation of stationary random signals is proposed, that can automatically provide an associated optimal estimate of the signals, only from an observed time series datum. First, the conventional method of power spectral estimation by smoothing periodgram is reviewed and the mean squared error of the normalized estimate is made clear, from the viewpoints of its bias and variance. Secondly, based on the fundamental nature of the statistics in a mutually reverse relation with respect to the smoothing bandwidth, a systematic method not only of adaptively determining the bandwidth but also of obtaining the optimal spectral estimate is presented, by newly introducing the evaluation indices of the statistics only from an observed datum. Finally, both the fundamental character and the effectiveness of the proposed method are illustrated by the fundamental results of computer simulations and power spectral estimation of measured heart sounds and noises.
