A generalized window method for spectral estimation

A novel approach to spectral estimation is presented. It starts by minimizing both an autocorrelation error measure and a planarity or smoothness measure of some statistics of the process. If spectral smoothness is selected, a window method depending on the variance of the autocorrelation estimates results. Classical windows are derived from a-priori assignments to the unknown variance. When the variance is estimated in terms of the available sample of the process, the window still depends on two parameters. An objective criterion for their selection is proposed and illustrated with an example. It is shown that the original minimization leads also into the Maximum Entropy method when the principle of maximum entropy is used as a measure of planarity of the density functions of the process.