The basis functions in the sampling-reconstruction procedure of Gaussian random fields

The problem of reconstruction of random Gaussian fields is investigated taking into consideration the character of basis functions. It's usual to concentrate on representing signals as weighted sums of complex exponential functions. Here we're going to study the more general case of linear combinations of any basis functions taking into account the conditional mean rule as the proposed method to analyses them. With this method is possible to investigate the basis function at the output of different low-pass reconstruction filters. For simplicity it is considered here two low-pass filters: the RC circuit and the two RC circuits in series. On the basis of this rule the reconstruction of random fields is described on the whole space domain. We apply the conditional mean function in order to obtain the reconstruction surface and the conditional variance function to describe the error reconstruction surfaces.