Explicit Full-Spark Gabor Windows with Quantitative Phase Retrieval

@misc{li2026explicit,
  title = {{Explicit Full-Spark Gabor Windows with Quantitative Phase Retrieval}},
  author = {Dongwei Li},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09614},
  eprint = {2609.09614},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09614},
}

TY  - UNPB
TI  - Explicit Full-Spark Gabor Windows with Quantitative Phase Retrieval
AU  - Dongwei Li
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.09614
UR  - https://arxiv.org/abs/2609.09614
AB  - We construct explicit algebraic finite Gabor windows that are simultaneously full spark and phase retrievable, with quantitative control of the self-ambiguity function. In every cyclic dimension, a constant--Chu window has an exactly computable ambiguity minimum of order N^−3/2; for N≥25, a two-site Chu repair has margin comparable to dN^−3/2 for every divisor d≤√N. A quantitative algebraic regularization, based on the high-degree specialization principle used in explicit full-spark Gabor constructions, imposes full spark while retaining a fixed proportion of a seed's ambiguity margin. These ingredients give explicit simultaneous constructions in every cyclic dimension and a factor-sensitive improvement when N has a divisor near √N. Further consequences include exact Chinese-remainder tensorization, optimal-order squarefree families, near-SIC prime regularization, lifted stability, and a finite cyclic Schrödinger construction.
ER  -