Abstract: A method of spectral estimation of a received radar signal wherein an image of the received radar signal is applied to windows of differing prolate spheroidal sequences to calculate multiple eigenspectra. The value of each of said sequences are multiplied with the radar signal, and the Fourier transforms of the products provide a plurality of realizations of orthogonal eigenspectra. The orthogonal eigenspectra are combined into a minimum variance, low bias estimate of the mean power spectrum and an estimate of a variance of said spectrum for each frequency in the spectrum to provide a more accurate estimate of back ground noise and to further improve detection performance.