Title | Antithetical Stratified Sampling Estimator for Filtering Signals with Discontinuities |
---|
Type | Journal article |
---|
Authors | Darawsheh, 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. |
---|
Keywords | Random sampling |
---|
| Filter estimator |
---|
| Uniform convergence rate |
---|
| Antithetical stratification |
---|
| Derivative discontinuities |
---|
Article number | 107910 |
---|
Journal | Signal Processing |
---|
Journal citation | 181 |
---|
ISSN | 0165-1684 |
---|
Year | 2021 |
---|
Publisher | Elsevier |
---|
| 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 online | 01 Dec 2020 |
---|
Published in print | Apr 2021 |
---|