Frequency-Shaped Randomized Sampling

This paper explores the use of discrete-time randomized sampling as a method to mitigate the effects of aliasing. Two distinct sampling architectures are presented along with second-order characterizations of the resulting sampling error. In the first, denoted simple randomized sampling, non-white sampling processes are shown to frequency-shape the error spectrum, so that its power is minimized in the band of interest. The design of non-white binary processes for use in randomized sampling is considered. In the second model, denoted filtered randomized sampling, a pre-filter, post-filter, and the sampling process are used to achieve a similar effect. In both cases, optimal mean-squared-error solutions are derived. Results from simulation are shown.