{
  "abstract": "Hyperbolic Frequency-Modulated (HFM) signals possess optimal Doppler tolerance, making them a central point in bioacoustic echolocation research. While the Doppler invariance of HFM signals is a known property, the explicit analytical calculation of their Wideband Ambiguity Function (WAF) is required. In this paper, we provide the exact mathematical derivations of the WAF for both the finite rectangular envelope and the pure hyperbolic signal. Furthermore, we introduce the HYPerbolicity Index (HYPI) to quantify time-frequency hyperbolicity across four different Time-Frequency Representations (TFRs). We establish that the Reassigned Spectrogram Representation is the least prone to HFM misidentification. Moreover, by evaluating the HYPI on foraging sequences of a bat species (Pipistrellus kuhlii). We demonstrate that the Hyperlocalized Wavelet Transform (HLT) offers the most consistent modulation extraction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Baudouin Le Gac"
    },
    {
      "name": "Nicolas Deloustal"
    },
    {
      "name": "Hervé Glotin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6tasy7g66qjvv.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "6tasy7g66qjvv",
  "issns": [],
  "landing_url": "https://hal.science/hal-05801151v2",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.info"
    ],
    [
      "hal",
      "0.phys"
    ],
    [
      "hal",
      "0.sdv"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05801151/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6tasy7g66qjvv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:58Z",
      "native_id": "hal-05801151",
      "source": "hal",
      "url": "https://hal.science/hal-05801151v2"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "hal:0.sdv",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "hal:0.phys",
      "subfield": "general"
    }
  ],
  "title": "Wideband Ambiguity Function Analysis And Quantification Protocols Of Hyperbolic Frequency-Modulated (Bio)Sonars",
  "title_text": "Wideband Ambiguity Function Analysis And Quantification Protocols Of Hyperbolic Frequency-Modulated (Bio)Sonars",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:58Z",
  "url": "https://research.draconitic.com/paper/6tasy7g66qjvv",
  "venue": "HAL",
  "versions": []
}