This paper considers an information aspect of the problem of the joint filtering and generalized extrapolation, when the output of observation channels (data transmission) is the realizations set of the processes with continuous and discrete time, which depend on both the current and the past values of unobservable process (useful signal). The relations defining time evolution of Shannon information are obtained. The particular problems of the memory channels information efficiency and optimal transmission of stochastic processes, with applying the general results are considered.