LOW TIME-BANDWIDTH PRODUCT SIGNAL PHASE ESTIMATION (LINEAR PROGRAMMING, RESOLUTION, HILBERT TRANSFORM).
Item
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Title
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LOW TIME-BANDWIDTH PRODUCT SIGNAL PHASE ESTIMATION (LINEAR PROGRAMMING, RESOLUTION, HILBERT TRANSFORM).
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Identifier
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AAI8423076
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identifier
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8423076
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Creator
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KEYBL, JAROSLAV EDVARD.
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Contributor
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George Eichmann
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Date
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1984
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Language
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English
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Publisher
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City University of New York.
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Subject
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Engineering, Electronics and Electrical
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Abstract
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A new method of resolving two closely spaced frequencies buried in noise is presented. The method involves knowing certain information about the signal a priori. This information is used to give a set of equations where there are less unknowns than there are equations. Since the system of equations is overdetermined, there are many possible solutions. We shall select the solution vector which yields the minimal norm of the residual error. By so doing, we are able to resolve the two frequencies of the signal beyond the limit imposed by the uncertainty principle of signal processing.;A second topic to be discussed is a new form of the Hilbert transform. An advantage of this new form is that it takes into account for signals that have been observed for short time durations. One use of the Hilbert transform is in phase estimation from magnitude measurements. This can be accomplished if the signal is causal and has zeros that occur only in the lower half of the complex z-plane. If zeros occur in the upper half of the z-plane, methods have to be introduced to reduce the effects of the zeros on the phase estimation. A new method for estimating the phase is shown where the spectrum is partitioned. All methods will be demonstrated via computer simulations.;The first chapter of this thesis contains material of an introductory nature. In Chapter 2, a new method of resolving two closely space frequencies when the time-bandwidth product is very low is presented. The method is shown to give favorable results under low signal-to-noise ratios. In the process of resolving the frequencies, we will obtain an estimate of the time signal. In Chapter 3, we introduce a new form of the Hilbert transform. With the new form of this transform we will show how the phase can be estimated from the magnitude of a signal, given that certain conditions are met. When these conditions cannot be met, modifications have to be performed before or after the estimate is obtained. Chapter 4 presents the general summary and conclusions obtained in this thesis.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
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Program
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Engineering
