Combinatorial signal processing
- We study the problem of interpolating all values of a discrete signal f of length N when d< N values are known, especially in the case when the Fourier transform of the signal is zero outside some prescribed index set J; these comprise the (generalized) bandlimited spaces B^J. The sampling pattern for f is specified by an index set I, and is said to be a universal sampling set if samples in the locations I can be used to interpolate signals from B^J for any J. When N is a prime power we give several characterizations of universal sampling sets, some structure theorems for such sets, an algorithm for their construction, and a formula that counts them. There are also natural applications to additive uncertainty principles. Universal sets are related to the invertible, but possibly poorly conditioned submatrices of a discrete Fourier transform matrix. At the other extreme, we study the problem of finding unitary submatrices of the discrete Fourier transform matrix. This problem is related to a diverse set of questions on idempotents on Z_N, tiling Z_N, difference graphs and maximal cliques. Each of these is related to the problem of interpolating a discrete bandlimited signal using an orthogonal basis.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Department of Electrical Engineering.
|Gill, John T III
|Gill, John T III
|Statement of responsibility
|Submitted to the Department of Electrical Engineering.
|Thesis (Ph.D.)--Stanford University, 2017.
- © 2017 by Tirumala Aditya Siripuram
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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