Antithetical Stratified Sampling Estimator for Filtering Signals with Discontinuities

Darawsheh, H. and Tarczynski, A. 2021. Antithetical Stratified Sampling Estimator for Filtering Signals with Discontinuities. Signal Processing. 181 107910. https://doi.org/10.1016/j.sigpro.2020.107910

TitleAntithetical Stratified Sampling Estimator for Filtering Signals with Discontinuities
TypeJournal article
AuthorsDarawsheh, H. and Tarczynski, A.
Abstract

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 the 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.

KeywordsRandom sampling
Filter estimator
Uniform convergence rate
Antithetical stratification
Derivative discontinuities
Article number107910
JournalSignal Processing
Journal citation181
ISSN0165-1684
Year2021
PublisherElsevier
The European Association for Signal Processing (EURASIP)
Accepted author manuscript
License
CC BY-NC-ND 4.0
File Access Level
Open (open metadata and files)
Digital Object Identifier (DOI)https://doi.org/10.1016/j.sigpro.2020.107910
Web address (URL)https://doi.org/10.1016/j.sigpro.2020.107910
Publication dates
Published online01 Dec 2020
Published in printApr 2021

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