Multidimensional Geometrical Signal Representation: Constructions and Applications
Lu, Yue
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https://hdl.handle.net/2142/81036
Description
Title
Multidimensional Geometrical Signal Representation: Constructions and Applications
Author(s)
Lu, Yue
Issue Date
2007
Doctoral Committee Chair(s)
Do, Minh N.
Department of Study
Electrical and Computer Engineering
Discipline
Electrical and Computer Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
We propose a computational procedure to find all alias-free quantized sampling lattices with minimum sampling density for a given frequency support. Central to this algorithm is a novel condition linking alias-free sampling with the Fourier transform of the indicator function defined on the frequency support. We also derive simple closed-form expressions of these Fourier transforms for a fairly general class of support regions consisting of arbitrary N-dimensional polytopes. With these closed-form expressions, the search for desired alias-free sampling lattices becomes a purely analytical and computational testing procedure.
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