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Spatio–Spectral Limiting on Redundant Cubes: A Case Study by Jeffrey A. Hogan; Joseph D. Lakey is a book available to read on EtoBox.

What is Spatio–Spectral Limiting on Redundant Cubes: A Case Study about?

The operator that first truncates to a neighborhood of the origin in the spatial domain then truncates to a neighborhood of zero in the spectral domain is investigated in the case of redundant cubes-Boolean cubes with added generators. This operator is self-adjoint on a space of spectrum-limited signals. Certain invariant subspaces of this iterated projection operator, in which eigenspaces lie, are studied for a specific example. These observations suggest a general structure of eigenspaces of spatio-spectral limiting on redundant cubes. ## Overview This work is part of a study of spatio-spectral limiting on finite graphs through specific structured graphs amenable to some level of combinatorial analysis. By spatial limiting we mean restriction to a vertex neighborhood in a connected graph, and by spectral limiting we mean, specifically, restriction to the span of eigenvectors of small eigenvalues of the graph Laplacian. Spatio-spectral limiting then refers to composition of a spatial-limiting operator and a spectral-limiting operator. These operators are analogues on graphs of time-and bandlimiting operators on R studied by Landau, Slepian, and Pollack beginning in the 1960s, e.g.

Author

Jeffrey A. Hogan; Joseph D. Lakey

Publisher

Springer International Publishing : Imprint: Birkhäuser

Published

2021

Language

EN

ISBN

9783030696368

Subjects

Mathematics, Stem