Shapes of Uncertainty in Spectral Graph Theory
Abstract
We present a flexible framework for uncertainty principles in spectral graph theory. In this framework, general filter functions modeling the spatial and spectral localization of a graph signal can be incorporated. It merges several existing uncertainty relations on graphs, among others the Landau-Pollak principle describing the joint admissibility region of two projection operators, and uncertainty relations based on spectral and spatial spreads. Using theoretical and computational aspects of the numerical range of matrices, we are able to characterize and illustrate the shapes of the uncertainty curves and to study the space-frequency localization of signals inside the admissibility regions.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2019
- DOI:
- 10.48550/arXiv.1909.10865
- arXiv:
- arXiv:1909.10865
- Bibcode:
- 2019arXiv190910865E
- Keywords:
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- Electrical Engineering and Systems Science - Signal Processing;
- Mathematics - Numerical Analysis
- E-Print:
- 21 pages, 9 figures, 1 table