Show simple item record

dc.contributor.advisorAlan V. Oppenheim.en_US
dc.contributor.authorDemirtas, Sefaen_US
dc.contributor.otherMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.en_US
dc.date.accessioned2014-09-19T21:32:55Z
dc.date.available2014-09-19T21:32:55Z
dc.date.copyright2014en_US
dc.date.issued2014en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/89989
dc.descriptionThesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014.en_US
dc.descriptionCataloged from PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (pages 175-180).en_US
dc.description.abstractFunctional composition, the application of one function to the results of another function, has a long history in the mathematics community, particularly in the context of polynomials and rational functions. This thesis articulates and explores a general framework for the use of functional composition in the context of signal processing. Its many potential applications to signal processing include utilization of the composition of simpler or lower order subfunctions to exactly or approximately represent a given function or data sequence. Although functional composition currently appears implicitly in a number of established signal processing algorithms, it is shown how the more general context developed and exploited in this thesis leads to significantly improved results for several important classes of functions that are ubiquitous in signal processing such as polynomials, frequency responses and discrete multivariate functions. Specifically, the functional composition framework is exploited in analyzing, designing and extending modular filters, separating marginalization computations into more manageable subcomputations and representing discrete sequences with fewer degrees of freedom than their length and region of support with implications for sparsity and efficiency.en_US
dc.description.statementofresponsibilityby Sefa Demirtas.en_US
dc.format.extent187 pagesen_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectElectrical Engineering and Computer Science.en_US
dc.titleFunctional composition and decomposition for signal processingen_US
dc.typeThesisen_US
dc.description.degreePh. D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
dc.identifier.oclc890130929en_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record