Optimum sampling vectors for Wiener filter noise reduction

Sampling is a very important and basic technique for signal processing. In the case that noise is added to a signal in the sampling process, we may use a reconstruction and noise reduction filter such as the Wiener filter. The Wiener filter provides a restored signal of which mean square error is minimized. However, the mean square error by the Wiener filter depends on the sampling vectors. We may have a freedom to construct sampling vectors. In this paper, we provide optimum sampling vectors under the condition that the Wiener filter is used for noise reduction for two cases wherein the noise is added before/after sampling. The sampling vectors provided in this paper may not be practical since they are very complicated. However, the minimum mean square error, which we provide theoretically, can be used for evaluating other sampling vectors. We provide all proofs of the theorems and lemmas. Furthermore, by experimental results, we show their advantages.