Optimal sampled-data reconstruction of stochastic signals with preview

The problem of H-2-optimal reconstruction of a continuous-time signal using a stable sampled-data filter is considered. The signal is corrupted by additive noise and is measured with preview of tau, i.e., it is known in advance over the interval T. This problem is equivalent to delayed signal reconstruction. A rigorous solution of the problem is presented on the basis of the parametric transfer function approach. Explicit expressions are given for the order of the optimal filter A lower bound is obtained for the cost function for,tau-->infinity, and it is shown that this bound depends on the ratio of the preview interval to the sampling period.