Abstract: In this paper signals of stationary random process superimposed with polynomial of unknown coefficients are considered and the necessary and sufficient conditions which the spectral characteristics in the equation used to estimate those coefficients of the poly-nomial as well as in the optimal prediction in the sense of mean-squared errors must satisfy are given. When the spectral density of the stationary random process is rational,it is shown that the problem of determining the optimal spectral characteristics can be reduced to that of solving a set of linear algebraic equations.