In the past decade, significant progress has been made to generalize classical tools from Fourier analysis to analyze and process signals defined on networks. In this paper, we propose a new framework for constructing Gabor-type frames for signals on graphs. Our approach uses general and flexible families of linear operators acting as translations. Compared to previous work in the literature, our methods yield the sharp bounds for the associated frames, in a broad setting that generalizes several existing constructions. We also examine how Gabor-type frames behave for signals defined on Cayley graphs by exploiting the representation theory of the underlying group. We explore how natural classes of translations can be constructed for Cayley graphs, and how the choice of an eigenbasis can significantly impact the properties of the resulting translation operators and frames on the graph.

在过去的十年中，从傅立叶分析到分析和处理网络上定义的信号的通用工具取得了重大进展。在本文中，我们提出了一种用于构造图上信号的Gabor型框架的新框架。我们的方法使用线性运算符的一般和灵活系列来充当转换。与文献中的先前工作相比，我们的方法在广泛概括了几种现有构造的前提下，为关联框架产生了清晰的界限。我们还通过利用基础群体的表示理论，研究Gabor型框架对于在Cayley图上定义的信号的行为。我们探讨了如何为Cayley图构造自然的翻译类，