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Discrete Sampling: A graph theoretic approach to Orthogonal Interpolation
We study the problem of finding unitary submatrices of the
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 and tiling
. 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
is a prime power, and we identify the challenges in generalizing to
arbitrary . Finally, we investigate some connections between graph
properties and the spectral-tile direction of the Fuglede conjecture.Comment: Submitted to IEEE Transactions on Information Theor