Maximum signal-to-noise ratio enhancement by averaging under a limited measurement time
Abstract
Averaging through repetitive measurement is a ubiquitous strategy for improving signal-to-noise ratio (SNR) and is commonly assumed to yield a √N enhancement with the number of repetitions N. This assumption, however, implicitly requires the signal amplitude to be independent of measurement duration. This condition does not generally hold in dynamical sensing systems with finite response time and a fixed measurement time. We derive a closed-form expression for the SNR enhancement factor by analytically accounting for the competition between statistical noise reduction and dynamical signal attenuation, and demonstrate the existence of a strict upper bound on the SNR enhancement. The enhancement factor is a non-monotonic function of N with a well-defined maximum at an optimal repetition number, beyond which further averaging degrades the SNR. Moreover, below a threshold set by the ratio of measurement time to response time, averaging yields no enhancement at all. These two regimes delimit where the conventional √N law breaks down. Experimental validation using nanomechanical gas sensing, with two receptor-analyte systems deliberately chosen to bracket this enhancement transition, confirms the theoretical predictions. Our results show that measurement time is a finite resource to be optimally partitioned between signal accumulation and averaging, and provide a quantitative guideline for selecting the repetition number in time-constrained sensing such as real-time and repetitive gas or odor detection.
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BibTeX
@misc{zhou2026maximum,
title = {{Maximum signal-to-noise ratio enhancement by averaging under a limited measurement time}},
author = {YingCheng Zhou and Kosuke Minami and Genki Yoshikawa and Gaku Imamura},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09744},
eprint = {2609.09744},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09744},
}
RIS
TY - UNPB
TI - Maximum signal-to-noise ratio enhancement by averaging under a limited measurement time
AU - YingCheng Zhou
AU - Kosuke Minami
AU - Genki Yoshikawa
AU - Gaku Imamura
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09744
UR - https://arxiv.org/abs/2609.09744
AB - Averaging through repetitive measurement is a ubiquitous strategy for improving signal-to-noise ratio (SNR) and is commonly assumed to yield a √N enhancement with the number of repetitions N. This assumption, however, implicitly requires the signal amplitude to be independent of measurement duration. This condition does not generally hold in dynamical sensing systems with finite response time and a fixed measurement time. We derive a closed-form expression for the SNR enhancement factor by analytically accounting for the competition between statistical noise reduction and dynamical signal attenuation, and demonstrate the existence of a strict upper bound on the SNR enhancement. The enhancement factor is a non-monotonic function of N with a well-defined maximum at an optimal repetition number, beyond which further averaging degrades the SNR. Moreover, below a threshold set by the ratio of measurement time to response time, averaging yields no enhancement at all. These two regimes delimit where the conventional √N law breaks down. Experimental validation using nanomechanical gas sensing, with two receptor-analyte systems deliberately chosen to bracket this enhancement transition, confirms the theoretical predictions. Our results show that measurement time is a finite resource to be optimally partitioned between signal accumulation and averaging, and provide a quantitative guideline for selecting the repetition number in time-constrained sensing such as real-time and repetitive gas or odor detection.
ER -