{
  "abstract": "Averaging through repetitive measurement is a ubiquitous strategy for improving signal-to-noise ratio (SNR) and is commonly assumed to yield a $\\sqrt{N}$ 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 $\\sqrt{N}$ 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09744",
  "author_total": 4,
  "authors": [
    {
      "name": "YingCheng Zhou"
    },
    {
      "name": "Kosuke Minami"
    },
    {
      "name": "Genki Yoshikawa"
    },
    {
      "name": "Gaku Imamura"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ad7aecc4nm9ry.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09744",
  "fulltext_url": null,
  "id": "ad7aecc4nm9ry",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09744",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.app-ph"
    ],
    [
      "openalex",
      "2208|Gas Sensing Nanomaterials and Sensors"
    ]
  ],
  "openalex": "W7212174889",
  "pdf_url": "https://arxiv.org/pdf/2609.09744",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ad7aecc4nm9ry.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.09744",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09744"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.app-ph",
      "subfield": "applied-instrumentation"
    }
  ],
  "title": "Maximum signal-to-noise ratio enhancement by averaging under a limited measurement time",
  "title_text": "Maximum signal-to-noise ratio enhancement by averaging under a limited measurement time",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:12Z",
  "url": "https://research.draconitic.com/paper/ad7aecc4nm9ry",
  "venue": "arXiv",
  "versions": []
}