Discrete-time randomized sampling

This paper explores the use of randomized sampling in implementing convolution in discrete-time with application to the areas of approximate filtering, low-power filter design, and hardware failure modeling. Three distinct randomized sampling methods are presented and additive error models as well as second-order error statistics are derived for these for both white and semi-correlated sampling processes. Discrete-time randomized sampling (RS) is then considered as a filter approximation method and conditions are derived under which RS-based approximations to the Wiener filter lead to a smaller mean-square estimation error than the best constrained LTI approximation. The tradeoff between power savings and output quality is also investigated for low-power applications. In addition, the RS framework is used to model a class of random hardware failures and algorithms are presented to improve the output SNR