The filtering problem for stochastic sequences consists in estimating the unobserved values of a stochastic sequence ξ( j) (signal) at a point j ∈ S from the observations at points j ∈ S the sequence ξ( j) with a noise sequence η( j) (i.e., observations of signal + noise sequence ξ( j) + η( j)). Usually, one has in mind the filtering estimator \( \widehat {\xi } (j) \) for which the mean-square error \( {{\textsf {E}}} |\xi ( j)-\widehat {\xi } (j) | ^ {2} \) is minimal over all estimators based on the observed values of the sequence ξ( j) + η( j), j ∈ S (the filtering is called linear if one restricts estimators to linear ones). One of the problems posed and solved was that of linear filtering of stationary stochastic sequences. Consider the problem in more details.