{
  "abstract": "STFT phase retrieval aims to reconstruct a signal from spectrogram magnitudes. While two compactly supported windows theoretically guarantee uniqueness, a complete algorithmic framework remains lacking. This paper systematically constructs numerical schemes for multi-window STFT phase retrieval. We theoretically provide a nonuniqueness counterexample for the single-window case. We then propose a two-window reconstruction algorithm based on Shannon interpolation and analytic square-root extraction. To overcome the instability of the global sign choice, we introduce a third window and a robust $K$-sign method that determines the sign locally. We also adapt SCR algorithm to the STFT setting. For the $K$-sign method, we establish deterministic stability on a finite contiguous block of frequency samples, with the contribution of the complementary tail explicitly included in the error bound. Numerical experiments validate the effectiveness of all schemes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35329",
  "author_total": 4,
  "authors": [
    {
      "name": "Ting Chen"
    },
    {
      "name": "Hanwen Lu"
    },
    {
      "name": "Wenchang Sun"
    },
    {
      "name": "Yutong Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9t8p6xaajngjv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35329",
  "fulltext_url": null,
  "id": "9t8p6xaajngjv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35329",
  "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",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7214798468",
  "pdf_url": "https://arxiv.org/pdf/2609.35329",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9t8p6xaajngjv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35329",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35329"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Algorithmic Implementation of Multi-Window STFT Phase Retrieval",
  "title_text": "Algorithmic Implementation of Multi-Window STFT Phase Retrieval",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/9t8p6xaajngjv",
  "venue": "arXiv",
  "versions": []
}