Year: 2026
Type: preprint
Abstract: 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 $N\ge25$, a two-site Chu repair has margin comparable to $dN^{-3/2}$ for every divisor $d\le\sqrt N$. 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 $\sqrt N$. Further consequences include exact Chinese-remainder tensorization, optimal-order squarefree families, near-SIC prime regularization, lifted stability, and a finite cyclic Schrödinger construction.
Source: arXiv (Cornell University)
Author: Li, Dongwei
Institution: Hefei University of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212154495