Quadratic Variational Framework for Signal Design on the 2-Sphere

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dc.contributor.authorWei, Liying
dc.contributor.authorKennedy, Rodney
dc.contributor.authorLamahewa, Tharaka
dc.date.accessioned2015-12-10T23:09:59Z
dc.date.issued2011
dc.date.updated2016-02-24T11:03:17Z
dc.description.abstractThis paper introduces a quadratic variational framework for solving a broad class of signal design problems on the 2-sphere. The functional, to be extremized, combines energy concentration measures using a weighting function in the spatial domain, multiplicative weights in the spectral domain, and a total energy constraint. This leads to two formulations of the signal design problem on the 2-sphere, one a Fredholm integral equation in the spatial domain and the other an infinite matrix equation in the spectral domain. The framework is illustrated by deriving the key equations for the two classical spatio-spectral concentration problems on the 2-sphere, and for an isotropic filter design that maximizes the filtered energy. In addition, using the proposed framework, we formulate a joint 3-D beamforming application which achieves optimal directivity and spatial resolution simultaneously.
dc.identifier.issn1053-587X
dc.identifier.urihttp://hdl.handle.net/1885/63528
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE Inc)
dc.sourceIEEE Transactions on Signal Processing
dc.subjectKeywords: 2-sphere; Directional derivative; Directivity; Energy concentration; Filter designs; Fredholm integral equations; isotropic convolution; Key equation; Matrix equations; Signal design; Spatial domains; Spatial resolution; Spectral domains; Total energy; un Directional derivative; isotropic convolution; uncertainty principle; unit sphere
dc.titleQuadratic Variational Framework for Signal Design on the 2-Sphere
dc.typeJournal article
local.bibliographicCitation.issue11
local.bibliographicCitation.lastpage5252
local.bibliographicCitation.startpage5243
local.contributor.affiliationWei, Liying, College of Engineering and Computer Science, ANU
local.contributor.affiliationKennedy, Rodney, College of Engineering and Computer Science, ANU
local.contributor.affiliationLamahewa, Tharaka, College of Engineering and Computer Science, ANU
local.contributor.authoremailu8607590@anu.edu.au
local.contributor.authoruidWei, Liying, u4271045
local.contributor.authoruidKennedy, Rodney, u8607590
local.contributor.authoruidLamahewa, Tharaka, u3995913
local.description.embargo2037-12-31
local.description.notesImported from ARIES
local.identifier.absfor090609 - Signal Processing
local.identifier.absseo970109 - Expanding Knowledge in Engineering
local.identifier.ariespublicationu4334215xPUB817
local.identifier.citationvolume59
local.identifier.doi10.1109/TSP.2011.2162506
local.identifier.scopusID2-s2.0-80054077324
local.identifier.thomsonID000297113500012
local.identifier.uidSubmittedByu4334215
local.type.statusPublished Version

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