- Title
- Spatio–Spectral Limiting on Replacements of Tori by Cubes
- Creator
- Hogan, Jeffrey A.; Lakey, Joseph D.
- Relation
- Mathematics Vol. 11, Issue 23, no. 4714
- Publisher Link
- http://dx.doi.org/10.3390/math11234714
- Publisher
- MDPI AG
- Resource Type
- journal article
- Date
- 2023
- Description
- A class of graphs is defined in which each vertex of a discrete torus is replaced by a Boolean hypercube in such a way that vertices in a fixed subset of each replacement cube are adjacent to corresponding vertices of a neighboring replacement cube. Bases of eigenvectors of the Laplacians of the resulting graphs are described in a manner suitable for quantifying the concentration of a low-spectrum vertex function on a single vertex replacement. Functions that optimize this concentration on these graphs can be regarded as analogues of Slepian prolate functions that optimize concentration of a bandlimited signal on an interval in the classical setting of the real line. Comparison to the case of a simple discrete cycle shows that replacement allows for higher concentration.
- Subject
- boolean cube; discrete torus; replacement graph; spatio-spectral limiting; spectral graph theory
- Identifier
- http://hdl.handle.net/1959.13/1496709
- Identifier
- uon:54216
- Identifier
- ISSN:2227-7390
- Rights
- x
- Language
- eng
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