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Signal Reconstruction From Nonuniform Samples Using Prolate Spheroidal Wave Functions: Theory and Application

Senay, Seda (2011) Signal Reconstruction From Nonuniform Samples Using Prolate Spheroidal Wave Functions: Theory and Application. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Nonuniform sampling occurs in many applications due to imperfect sensors, mismatchedclocks or event-triggered phenomena. Indeed, natural images, biomedical responses andsensor network transmission have bursty structure so in order to obtain samples that correspondto the information content of the signal, one needs to collect more samples when thesignal changes fast and fewer samples otherwise which creates nonuniformly distibuted samples.On the other hand, with the advancements in the integrated circuit technology, smallscale and ultra low-power devices are available for several applications ranging from invasivebiomedical implants to environmental monitoring. However the advancements in the devicetechnologies also require data acquisition methods to be changed from the uniform (clockbased, synchronous) to nonuniform (clockless, asynchronous) processing. An important advancementis in the data reconstruction theorems from sub-Nyquist rate samples which wasrecently introduced as compressive sensing and that redenes the uncertainty principle. Inthis dissertation, we considered the problem of signal reconstruction from nonuniform samples.Our method is based on the Prolate Spheroidal Wave Functions (PSWF) which can beused in the reconstruction of time-limited and essentially band-limited signals from missingsamples, in event-driven sampling and in the case of asynchronous sigma delta modulation.We provide an implementable, general reconstruction framework for the issues relatedto reduction in the number of samples and estimation of nonuniform sample times. We alsoprovide a reconstruction method for level crossing sampling with regularization. Another way is to use projection onto convex sets (POCS) method. In this method we combinea time-frequency approach with the POCS iterative method and use PSWF for the reconstructionwhen there are missing samples. Additionally, we realize time decoding modulationfor an asynchronous sigma delta modulator which has potential applications in low-powerbiomedical implants.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Senay, Sedases62@pitt.eduSES62
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairChaparro, Luis Flfch@pitt.eduLFCH
Committee MemberManfredi, Juanmanfredi@pitt.eduMANFREDI
Committee MemberSun, Minguidrsun@pitt.eduDRSUN
Committee MemberLoughlin, Patrickloughlin@pitt.eduLOUGHLIN
Committee MemberSclabassi, Robert
Committee MemberMao, Zhi-Hongmaozh@engr.pitt.eduZHM4
Date: 27 June 2011
Date Type: Completion
Defense Date: 7 April 2011
Approval Date: 27 June 2011
Submission Date: 31 March 2011
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Swanson School of Engineering > Electrical Engineering
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: compressive sensing; nonuniform sampling; prolate spheroidal wave functions
Other ID:, etd-03312011-173837
Date Deposited: 10 Nov 2011 19:33
Last Modified: 15 Nov 2016 13:38


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