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Sampling Density for Multi-window STFT Phase Retrieval
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 bbC2. We prove that the multi-window magnitude samples uniquely determine every signal in L2(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].
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BibTeX
@misc{sun2026sampling,
title = {{Sampling Density for Multi-window STFT Phase Retrieval}},
author = {Wenchang Sun and Mengxuan Zhou},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04877},
eprint = {2611.04877},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04877},
}
RIS
TY - UNPB
TI - Sampling Density for Multi-window STFT Phase Retrieval
AU - Wenchang Sun
AU - Mengxuan Zhou
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04877
UR - https://arxiv.org/abs/2611.04877
AB - 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].
ER -