{
  "abstract": "Root-MUSIC is a spectral estimation algorithm that approximates the unknown signal frequencies by constructing a high-degree polynomial and finding a subset of roots which are closest to the complex unit circle. Previous works found asymptotic expectation formulas for the performance of Root-MUSIC under the implicit assumption that the aforementioned root selection criterion does not select extraneous roots -- those which are unrelated to the correct parameters. This paper removes the need for this assumption by showing all extraneous roots lie outside an annulus of a certain thickness and therefore are not selected by the algorithm. This paper also provides sharp and non-asymptotic error bounds for the correct roots in terms of fundamental model parameters. All results hold under a natural separation condition on the correct signal frequencies and are applicable in both the single- and multi-snapshot models. Numerical simulations confirm our theory. The main mathematical insight of this paper is a geometric property of the Root-MUSIC polynomial: its correct roots are highly stable to noise while its extraneous roots must lie outside of an annulus.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.04003",
  "author_total": 2,
  "authors": [
    {
      "name": "Hana Huber"
    },
    {
      "name": "Weilin Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8g9kzty7hts36.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.04003",
  "fulltext_url": null,
  "id": "8g9kzty7hts36",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.04003",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
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      "arxiv",
      "eess.SP"
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    [
      "arxiv",
      "math.IT"
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      "openalex",
      "1711|Direction-of-Arrival Estimation Techniques"
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  "openalex": "W7163508844",
  "pdf_url": "https://arxiv.org/pdf/2606.04003",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8g9kzty7hts36.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:43Z",
      "native_id": "2606.04003",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.04003"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "A sharp analysis of Root-MUSIC: locations of correct and extraneous roots",
  "title_text": "A sharp analysis of Root-MUSIC: locations of correct and extraneous roots",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:43Z",
  "url": "https://research.draconitic.com/paper/8g9kzty7hts36",
  "venue": "arXiv",
  "versions": []
}