论文标题
$ \ mathbb {z} $，$ \ mathbb {z} _d $和$ \ mathbb {r}^d $上的sTFT阶段检索条件
Injectivity conditions for STFT phase retrieval on $\mathbb{Z}$, $\mathbb{Z}_d$ and $\mathbb{R}^d$
论文作者
论文摘要
我们研究了组$ \ mathbb {z} $，$ \ mathbb {z} _d $和$ \ mathbb {r}^d $的短时傅立叶变换的阶段检索问题。众所周知，一旦窗口的歧义函数无济于事，则可以进行相位检索。但是，对于不符合这种情况的窗口的结果很少。本文的目的是通过更通用的窗口建立新的和完整的阶段检索特征，并将其与现有结果进行比较。对于固定的窗口，我们的独特条件通常仅取决于信号的支撑，因此很容易理解。此外，我们通过查看沿途的各种示例来讨论新结果的清晰度。
We study the phase retrieval problem for the short-time Fourier transform on the groups $\mathbb{Z}$, $\mathbb{Z}_d$ and $\mathbb{R}^d$. As is well-known, phase retrieval is possible, once the window's ambiguity function vanishes nowhere. However, there are only few results for windows which don't meet this condition. The goal of this paper is to establish new and complete characterizations for phase retrieval with more general windows and compare them to existing results. For a fixed window, our uniqueness conditions usually only depend on the signal's support and are therefore easily comprehensible. Additionally, we discuss sharpness of both new and existing results by looking at various examples along the way.
