Maximum entropy algorithm for spectral estimation problem with gaps

The maximum entropy approach to the solution of power density estimation problems with gaps is studied in context of the trigonometric moment problem with gaps. We establish the necessary and sufficient conditions for the existence of solution and describe all solutions of the spectral density estimation problem. The considered approach allows us to describe any possible extrapolation of the autocorrelation function agrees with a set of known values and a priori information about spectral power density and to introduce into consideration the new definition of the entropy functional which coincides with the generally used one in case of conventional spectral power density estimation problem. The effective algorithm to construct maximum entropy solution of the power density estimation problem with gaps is proposed