A Linear, Time-Varying System Framework for Bandlimited Signal Extrapolation
Diethorn, Eric John
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https://hdl.handle.net/2142/69371
Description
Title
A Linear, Time-Varying System Framework for Bandlimited Signal Extrapolation
Author(s)
Diethorn, Eric John
Issue Date
1987
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Abstract
A Fourier theory for modeling, analyzing, and designing linear, time-varying systems is used to study several aspects of bandlimited signal extrapolation, the problem of reconstructing the whole of a bandlimited signal from a known piece. The extrapolation of both continuous-time and discrete-time signals is considered.
The principal component of the approach is that of modeling the extrapolation process as a linear, time-varying operation on the known data, where the operator is defined by a linear, time-varying system--the extrapolation system. A frequency-domain representation facilitates the characterization of this system. In particular, this representation provides clear, visual evidence of the extreme noise-sensitivity associated with extrapolation--one of the most pressing issues of study today. A least-squares approximation procedure for designing extrapolation systems is also developed. This design methodology is shown to unify a large class of well-documented algorithms for extrapolating both continuous-time and discrete-time data. New techniques for extrapolating data in the presence of noise are also developed.
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