A parametric set of nonlinear methods of spectral estimations

A novel rigorous approach to the spectral density estimation problem based on the trigonometric moment problem technique is considered. Using the trigonometric moment problem results, all possible extrapolations of the autocorrelation function, which are in agreement with a set of known values are found. A wide set of spectral estimators is described in terms of polynomials orthogonal with respect to the given autocorrelation sequence. The parametric representation for this set is given.