{
  "abstract": "We study phase retrieval for multi-window short-time Fourier transforms with windows given by complex linear combinations of the first two normalized Hermite functions. Assume that the family of window coefficient vectors does phase retrieval in $\\bbC^2$. We prove that the multi-window magnitude samples uniquely determine every signal in $L^2(\\bbR)$ up to a global phase whenever the sampling set is separated with lower Beurling density greater than $2$, or is a translated lattice with density at least $2$. Moreover, we show that the sampling density is the best possible, which improves a result in [P.~Grohs, L.~Liehr, and M.~Rathmair. Multi-window {STFT} phase retrieval: lattice uniqueness, J. Funct. Anal., 288(3): Paper No. 110733, 23, 2025].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04877",
  "author_total": 2,
  "authors": [
    {
      "name": "Wenchang Sun"
    },
    {
      "name": "Mengxuan Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/20hs5w5eww3tt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04877",
  "fulltext_url": null,
  "id": "20hs5w5eww3tt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04877",
  "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",
      "math.CA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04877",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/20hs5w5eww3tt.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04877",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04877"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sampling Density for Multi-window STFT Phase Retrieval",
  "title_text": "Sampling Density for Multi-window STFT Phase Retrieval",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/20hs5w5eww3tt",
  "venue": "arXiv",
  "versions": []
}