{
  "abstract": "The article examines alpha-rhythm spindles. The importance of studying alpha rhythm spindles for improving the reliability of nervous system diagnostics is substantiated. The analysis employs a mathematical framework based on the Hilbert transform as well as spectral analysis based on the classical Fourier transform. Using the Hilbert transform, the instantaneous frequency of the spindles is determined. It is shown that a spindle is not an amplitude-modulated oscillation and a spindle can be described using the beating method. Two frequencies are obtained that determine the frequency composition of the spindles. It is shown that the beating method is more accurate compared to the Fourier transform.",
  "abstract_shown": true,
  "affiliations": [
    "Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str., Block 8, 1113 Sofia, Bulgaria",
    "Department of Design and Operation of Electronic Devices, Kharkiv National University of Radio Electronics, 14 Nauky Ave., 61023 Kharkiv, Ukraine",
    "Department of Mathematics and Informatics, University of Mining and Geology, Boyan Kamenov Str., Student Complex, 1700 Sofia, Bulgaria",
    "Department of Sleep Medicine, Institute of Neurology, Psychiatry and Narcology, National Academy of Medical Sciences, 46 Akademika Pavlova Str., 61068 Kharkiv, Ukraine"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Oksana Kharchenko",
      "orcid": "0000-0002-1553-0966"
    },
    {
      "affs": [
        1
      ],
      "name": "Volodymyr Chumakov",
      "orcid": "0000-0001-6418-8688"
    },
    {
      "affs": [
        0,
        2
      ],
      "name": "Zlatinka Kovacheva",
      "orcid": "0000-0001-7401-3072"
    },
    {
      "affs": [
        3
      ],
      "name": "Liudmyla Zabrodina",
      "orcid": "0000-0001-8756-3479"
    },
    {
      "affs": [
        0
      ],
      "name": "Velin Andonov",
      "orcid": "0000-0001-5055-3867"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1grsk14dexh6t.bib",
  "cited_by": 0,
  "doi": "10.3390/axioms15110820",
  "fulltext_url": null,
  "id": "1grsk14dexh6t",
  "issns": [
    "2075-1680"
  ],
  "landing_url": "https://www.mdpi.com/2075-1680/15/11/820",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/1grsk14dexh6t.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T00:20:50Z",
      "native_id": "10.3390/axioms15110820",
      "source": "crossref",
      "url": "https://www.mdpi.com/2075-1680/15/11/820"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "journal-openalex:F26",
      "subfield": "general"
    }
  ],
  "title": "A Novel Approach to Alpha Spindle Analysis",
  "title_text": "A Novel Approach to Alpha Spindle Analysis",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T00:21:06Z",
  "url": "https://research.draconitic.com/paper/1grsk14dexh6t",
  "venue": "Axioms",
  "versions": []
}