Discrete Sampling: A Graph Theoretic Approach to Orthogonal Interpolation

Siripuram, Aditya and Wu, William D and Osgood, Brad (2019) Discrete Sampling: A Graph Theoretic Approach to Orthogonal Interpolation. IEEE Transactions on Information Theory, 65 (12). pp. 8119-8130. ISSN 0018-9448

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Abstract

We study the problem of finding unitary submatrices of the N × N discrete Fourier transform matrix, in the context of interpolating a discrete bandlimited signal using an orthogonal basis. This problem is related to a diverse set of questions on idempotents on ZN and tiling ZN. In this work, we establish a graph-theoretic approach and connections to the problem of finding maximum cliques. We identify the key properties of these graphs that make the interpolation problem tractable when N is a prime power, and we identify the challenges in generalizing to arbitrary N. Finally, we investigate some connections between graph properties and the spectral-tile direction of the Fuglede conjecture.

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IITH Creators:
IITH CreatorsORCiD
Siripuram, AdityaUNSPECIFIED
Item Type: Article
Uncontrolled Keywords: circulant graphs, Discrete Fourier transforms, interpolation, perfect graphs, Indexed in Scopus
Subjects: Electrical Engineering
Divisions: Department of Electrical Engineering
Depositing User: Team Library
Date Deposited: 13 Jan 2020 10:34
Last Modified: 13 Jan 2020 10:34
URI: http://raiith.iith.ac.in/id/eprint/7313
Publisher URL: http://doi.org/10.1109/TIT.2019.2934688
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