On general filtering problem of stationary processes with fixed transformation

A fixed transformation are given for one-dimensional stationary processes in this paper. Based on this, we propose a general filtering problem of stationary processes with fixed transformation. Finally, on a stationary processes with no any additional conditions, we get the spectral characteristics of P H η ( t ) ξ in the space L2(FX(dλ)), and then we calculate the value of the best predict quantity Q of the general filtering problem.