论文标题
从离散的完整性转化为短期傅立叶变换的无相位采样
From completeness of discrete translates to phaseless sampling of the short-time Fourier transform
论文作者
论文摘要
我们通过探索与离散翻译的完整性问题的联系来研究短期傅立叶变换阶段检索中的唯一性问题。具体来说，我们证明，$ l^2（k）$的功能与$ k \ subseteq \ mathbb {r}^d $ compact在其短期傅立叶变换的窗口函数$ g $的短时间无质量晶格示例中唯一确定，前提是$ g $。通过在紧凑型集合中在Banach功能空间中证明离散系统的完整性语句，我们获得了在已知的高斯窗口制度以外的晶格上进行无量抽样的新独特语句。我们的结果适用于大量的窗口功能，这些功能与时频分析和应用相关。
We study the uniqueness problem in short-time Fourier transform phase retrieval by exploring a connection to the completeness problem of discrete translates. Specifically, we prove that functions in $L^2(K)$ with $K \subseteq \mathbb{R}^d$ compact, are uniquely determined by phaseless lattice-samples of its short-time Fourier transform with window function $g$, provided that specific density properties of translates of $g$ are met. By proving completeness statements for systems of discrete translates in Banach function spaces on compact sets, we obtain new uniqueness statements for phaseless sampling on lattices beyond the known Gaussian window regime. Our results apply to a large class of window functions, which are relevant in time-frequency analysis and applications.
