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arXiv · 2605.20527

$L^2$-Stability for STFT phase retrieval

Susanna Bertolini·Jaume de Dios Pont·Ben Pineau·Mitchell A. Taylor·João P. G. Ramos
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Abstract

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.

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Susanna Bertolini, Jaume de Dios Pont, Ben Pineau, Mitchell A. Taylor, João P. G. Ramos. 2026-05-19. $L^2$-Stability for STFT phase retrieval. https://arxiv.org/abs/2605.20527

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