High Rate Reconstruction of Random Signals from Generalized Samples

We address the problem of reconstructing a random signal from samples of its filtered version using a given interpolation kernel. In order to reduce the mean squared error (MSE) when using a non-optimal interpolation kernel we propose using a scheme with reconstruction rate that is greater than the sampling rate. A digital correction system that processes the samples prior to their multiplication with the shifts of the interpolation kernel is developed. This system is constructed such that the reconstructed signal is the linear minimum MSE estimate of the original signal given its samples. Simulations, as well as theoretical arguments, confirm the reduction in MSE with respect to a system with equal rates of sampling and reconstruction. An explicit condition is also derived such that the optimal MSE is achieved with the given kernel.