Statistical Aspects of Sampling for Noisy and Grouped Data

Abstract

The problem of recovering a signal in the class of bandlimited functions from its sampled values observed in the presence of noise is studied. We consider a situation when discrete data points are condensed into groups and the problem of signal reconstruction from such a reduced data set is addressed. The data grouping is necessary for computer rounding errors and in telecommunication systems as a method for data compression. The statistical accuracy of the proposed signal recovering techniques is examined. These results are used to provide an understanding of the size of compression allowed to achieve a given level of accuracy.