The adaptive linear filtering of a digital television signal, treated as an additive mixture of a useful signal and a noise, is analyzed. Digital filters are synthesized which operate in either the spectral domain or the spatial domain on the basis of a composite criterion involving the mean square error and the overall sharpness of the reconstructed image. An algorithm is proposed for the adaptation of these filters. The number of computational operations required for performing a filtering is found. Some representative block diagrams of adaptive filters for real-time suppression of a fluctuational noise in a digital television signal are constructed.