  The problem of the mean-square optimal linear estimation of functionals which
depend on the unknown values of a stationary stochastic sequence from
observations of the sequence with noise is considered. In the case of spectral
certainty, where the spectral densities of the sequences are exactly known, we
propose formulas for calculating the spectral characteristic and value of the
mean-square error of the estimate, which are determined using the Fourier
coefficients of some functions from the spectral densities. The minimax-robust
method of estimation is applied in the case of spectral uncertainty, where the
spectral densities are not exactly known, but a class of admissible spectral
densities is given. Formulas for determining the least favorable spectral
densities and the minimax-robust spectral characteristics of the optimal
estimates of the functionals are proposed for some specific classes of
admissible spectral densities.
