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.
Bibliographical noteFunding Information:
M. Ghandehari was supported by NSF Grant (DMS–1902301) while this project was being completed. D. Guillot was partially supported by a collaboration grant for mathematicians from the Simons Foundation (#526851), and by a Strategic Initiative grant from the University of Delaware Research Foundation (#18A00532). We sincerely thank the anonymous reviewers for reading the manuscript and suggesting improvements.
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
- Cayley graph
- Gabor frame
- Graph signal