Sampling and distortion tradeoffs for bandlimited periodic signals

In this paper, the optimal sampling strategies (uniform or nonuniform) and distortion tradeoffs for stationary bandlimited periodic signals are studied. We justify and use both the average and variance of distortion as the performance criteria. To compute the optimal distortion, one needs to find the optimal sampling locations, as well as the optimal pre-sampling filter. A complete characterization of the optimal distortion for the rates lower than half the Landau rate is provided. It is shown that nonuniform sampling outperforms uniform sampling. In addition, this nonuniform sampling is robust with respect to missing samples. Next, for the rates higher than half the Landau rate, we find bounds that are shown to be tight for some special cases. An extension of the results for random discrete periodic signals is discussed, with simulation results indicating that the intuitions from the continuous domain carry over to the discrete domain.