Random sampling of random processes: Mean-square comparison of various interpolators

This paper compares the relative merits (in the mean-square sense) of the zero-order hold, the exponential hold, and the polygonal hold vs. a linear nonrealizable interpolation procedure. This comparison is done for three sampling schemes; periodic sampling, periodic sampling with skips, and Poisson sampling. General expressions for the mean-square error are given in terms of the second-order statistics of the weakly stationary sampled process and in terms of the statistics associated with the sampling procedure. For purposes of illustration, the sampled process is assumed to be either a wide-sense Markov process or a band-limited white noise process; the results obtained for these cases are plotted and lead to simple conclusions which are of interest in the theory of interpolation.