- Title
- Spatio-spectral limiting on discrete tori: adjacency invariant spaces
- Creator
- Hogan, Jeffrey A.; Lakey, Joseph D.
- Relation
- Sampling Theory, Signal Processing, and Data Analysis Vol. 19, Issue 14
- Publisher Link
- http://dx.doi.org/10.1007/s43670-021-00014-2
- Publisher
- Birkhaeuser Science
- Resource Type
- journal article
- Date
- 2021
- Description
- Discrete tori are ZmN thought of as vertices of graphs CmN whose adjacencies encode the Cartesian product structure. Space-limiting refers to truncation to a symmetric path neighborhood of the zero element and spectrum-limiting in this case refers to corresponding truncation in the isomorphic Fourier domain. Composition spatio-spectral limiting (SSL) operators are analogues of classical time and band limiting operators. Certain adjacency-invariant spaces of vectors defined on ZmN are shown to have bases consisting of Fourier transforms of eigenvectors of SSL operators. We show that when m= 3 or m= 4 , all eigenvectors of SSL arise in this way. We study the structure of corresponding invariant spaces when m= 5 and give an example to indicate that the relationship between eigenvectors of SSL and the corresponding adjacency-invariant spaces should extend to m= 5.
- Subject
- discrete tori; time and band limiting; spatio-spectral limiting; graph laplacian; graph fourier transform
- Identifier
- http://hdl.handle.net/1959.13/1435207
- Identifier
- uon:39638
- Identifier
- ISSN:2730-5716
- Language
- eng
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