An Efficient Formula for Estimating the Generalized Moments of the Power Spectral Density (PSD) Without Computing the Fourier Transform

Estimates of the moments of the power spectral density (PSD) are derived from a rapidly converging series of weighted samples of the autocorrelation function (ACF). As a result of the rapid convergence of the weighting coefficients of this series, accurate PSD moment estimates are obtained from a small number of ACF samples without computing the Fourier transform of the time series, thereby greatly reducing the computational requirements for generatiing the generalized moments of the PSD. The general expression for the moment generating series is presented along with explicit expressions for computing the first four moments from which mean, variance, skewness, and kurtosis of the PSD are obtained.