$L^2$-Stability for STFT phase retrieval
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918513068736512 |
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| author | Bertolini, Susanna Pont, Jaume de Dios Pineau, Ben Taylor, Mitchell A. Ramos, João P. G. |
| author_facet | Bertolini, Susanna Pont, Jaume de Dios Pineau, Ben Taylor, Mitchell A. Ramos, João P. G. |
| contents | We prove that the short-time Fourier transform with Gaussian window performs $L^2$-local stable phase retrieval at the constant function. The proof involved significant interplay between mathematicians and LLMs. An autoformalization in Lean 4 of an extension of our result to $L^2$-local stable phase retrieval for all Hermite windows and all elements in the finite span of the canonical basis vectors is also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20527 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $L^2$-Stability for STFT phase retrieval Bertolini, Susanna Pont, Jaume de Dios Pineau, Ben Taylor, Mitchell A. Ramos, João P. G. Functional Analysis Classical Analysis and ODEs We prove that the short-time Fourier transform with Gaussian window performs $L^2$-local stable phase retrieval at the constant function. The proof involved significant interplay between mathematicians and LLMs. An autoformalization in Lean 4 of an extension of our result to $L^2$-local stable phase retrieval for all Hermite windows and all elements in the finite span of the canonical basis vectors is also presented. |
| title | $L^2$-Stability for STFT phase retrieval |
| topic | Functional Analysis Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2605.20527 |