An FIR estimation filter based on the sampling theorem

The estimation of noise-perturbed bandlimited stochastic signal samples by FIR filtering is considered. The mean-square error of the estimate is used as the criterion of performance. We contrast three types of filters: all-pass, a sampling-theorem-based filter, and the minimum mean-square error (Wiener) filter. Although the Wiener filter is linearly optimal, its design requires detailed knowledge of the processes' second-order statistics. The sampling theorem filter does not. For large signal-to-noise ratios and large filter orders, the two filters perform nearly identically asymptotically. Furthermore, we demonstrate that for a fixed filter order, there exists an optimal sampling rate which decreases with increasing signal-to-noise ratio.