The problem of optimal linear estimation of a functional from unknown values ​​of a stationary stochastic process based on observations of a process with noise is investigated. Formulas are found for calculating the root mean square error and spectral characteristic of the optimal functional estimate provided that the spectral densities of the processes are known. In the case when the form of the spectral densities is unknown, but sets of admissible spectral densities are given, the minimax estimation method is applied. For the given sets of admissible spectral densities, the least favorable spectral densities and minimax spectral characteristics of the optimal linear estimation of the functional are determined.