Algorithmic Implementation of Multi-Window STFT Phase Retrieval

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.

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BibTeX RIS

BibTeX

@misc{chen2026algorithmic,
  title = {{Algorithmic Implementation of Multi-Window STFT Phase Retrieval}},
  author = {Ting Chen and Hanwen Lu and Wenchang Sun and Yutong Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35329},
  eprint = {2609.35329},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35329},
}

RIS

TY  - UNPB
TI  - Algorithmic Implementation of Multi-Window STFT Phase Retrieval
AU  - Ting Chen
AU  - Hanwen Lu
AU  - Wenchang Sun
AU  - Yutong Zhao
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35329
UR  - https://arxiv.org/abs/2609.35329
AB  - 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.
ER  -

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