Antithetical stratified sampling estimator for filtering signals with discontinuities

A novel approach to signal filtering using digital alias-free signal processing (DASP) is presented in this paper. We propose an unbiased, fast-converging estimator of the output of a finite impulse response (FIR) continuous-time filter. The estimator processes 2N signal samples collected with the use of random antithetical stratified (AnSt) sampling technique. To assess the estimator convergence rate as a function of N, we consider various forms of smoothness of the input signal, filter impulse response and windowing function. The cases are piecewise-continuous second-order derivative (SOD), piecewise-continuous first-order derivative (FOD) and piecewise-continuous zero-order derivative (ZOD). In each case we assume that the respective derivative has a finite number of bounded discontinuities. We prove that the proposed estimator converges to the true filter output at the rate of N-5 in the first case. But for the other two the rate drops to N-4 and N-2 respectively. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This paper presents a novel approach to signal filtering using digital alias-free signal processing (DASP). An unbiased, fast-converging estimator of the output of a finite impulse response (FIR) continuous-time filter is proposed, which processes 2N signal samples collected with a random antithetical stratified (AnSt) sampling technique. The convergence rate of the estimator is assessed as a function of N, with different forms of smoothness of the input signal, filter impulse response, and windowing function considered.