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Waveform Design with Time and Frequency Constraints for Optimal Detection of Elastic Objects

Hamschin, Brandon Michael (2011) Waveform Design with Time and Frequency Constraints for Optimal Detection of Elastic Objects. Master's Thesis, University of Pittsburgh.

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    Abstract

    In active sonar, the goal is to learn about an object or environment by transmitting a sound and processing the echo. The sound we choose to transmit will determine what we learn about the object, much like the choice of question we ask a person will determine what we learn from them. Thus, designing the best (i.e. optimal) transmit waveform is a longstanding area of research that remains active since different environments and ever evolving operational objectives weigh heavily on how we define optimality.In this work we extend a recent result by Kay that gives the optimal transmit signal that maximizes the probability of detecting an elastic object in the presence of Gaussian reverber- ation and additive Gaussian interference. Kay's solution specifies the spectral magnitude for the optimal transmit waveform, and hence there is an unlimited number of "optimal" wave- forms that can be transmitted, all with the same spectral magnitude but differing in terms of time domain characteristics such as duration and peak power. We extend Kay's approach in order to obtain a unique optimal waveform by incorporating time-domain constraints into two optimization-based problem formulations. These two problem formulations lead to new and complementary signal design approaches that impose temporal duration constraints while preserving, to varying degrees, the optimality inherent in the spectral magnitude.


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    Item Type: University of Pittsburgh ETD
    Creators/Authors:
    CreatorsEmailORCID
    Hamschin, Brandon Michaelbmh161@gmail.com
    ETD Committee:
    ETD Committee TypeCommittee MemberEmailORCID
    Committee ChairLoughlin, Patrick Jloughlin@pitt.edu
    Committee MemberEl-Jaroudi, Amroamro@pitt.edu
    Committee MemberJacobs, Stevenspj1@pitt.edu
    Title: Waveform Design with Time and Frequency Constraints for Optimal Detection of Elastic Objects
    Status: Unpublished
    Abstract: In active sonar, the goal is to learn about an object or environment by transmitting a sound and processing the echo. The sound we choose to transmit will determine what we learn about the object, much like the choice of question we ask a person will determine what we learn from them. Thus, designing the best (i.e. optimal) transmit waveform is a longstanding area of research that remains active since different environments and ever evolving operational objectives weigh heavily on how we define optimality.In this work we extend a recent result by Kay that gives the optimal transmit signal that maximizes the probability of detecting an elastic object in the presence of Gaussian reverber- ation and additive Gaussian interference. Kay's solution specifies the spectral magnitude for the optimal transmit waveform, and hence there is an unlimited number of "optimal" wave- forms that can be transmitted, all with the same spectral magnitude but differing in terms of time domain characteristics such as duration and peak power. We extend Kay's approach in order to obtain a unique optimal waveform by incorporating time-domain constraints into two optimization-based problem formulations. These two problem formulations lead to new and complementary signal design approaches that impose temporal duration constraints while preserving, to varying degrees, the optimality inherent in the spectral magnitude.
    Date: 24 June 2011
    Date Type: Completion
    Defense Date: 28 March 2011
    Approval Date: 24 June 2011
    Submission Date: 05 April 2011
    Access Restriction: No restriction; The work is available for access worldwide immediately.
    Patent pending: No
    Institution: University of Pittsburgh
    Thesis Type: Master's Thesis
    Refereed: Yes
    Degree: MSEE - Master of Science in Electrical Engineering
    URN: etd-04052011-212244
    Uncontrolled Keywords: Detection Theory; Digital Signal Processing; Optimization; Waveform Design; Classification Theory; Estimation Theory
    Schools and Programs: Swanson School of Engineering > Electrical Engineering
    Date Deposited: 10 Nov 2011 14:34
    Last Modified: 20 Apr 2012 10:00
    Other ID: http://etd.library.pitt.edu/ETD/available/etd-04052011-212244/, etd-04052011-212244

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