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Discrete Sampling: A graph theoretic app...
Siripuram, Aditya...

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Discrete Sampling: A graph theoretic approach to Orthogonal Interpolation by Siripuram, Aditya ( Author )
Lemonjar Open Access
Australian National University
06-09-2023
We study the problem of finding unitary submatrices of the $N \times N$ 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 $\mathbb{Z}_N$ and tiling $\mathbb{Z}_N$. 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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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1411.7086
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