Explicit Full-Spark Gabor Windows with Quantitative Phase Retrieval

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 $N\ge 25$, a two-site Chu repair has margin comparable to $d{N}^{-3/2}$ 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.