Spatio-spectral Analysis on the Sphere Using Spatially Localized Spherical Harmonics Transform
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Khalid, Zubair; Sadeghi, Parastoo; Kennedy, Rodney; Durrani, Salman
Description
This correspondence studies a spatially localized spectral transform for signals on the unit sphere, which we call spatially localized spherical harmonics transform (SLSHT). For a systematic treatment, we explicitly express the transform in terms of rotated versions of an azimuthally symmetric window function and introduce the spatio-spectral SLSHT distribution with a succinct matrix representation. We present guidelines for the choice of the window function in the SLSHT, based on the inherent...[Show more]
dc.contributor.author | Khalid, Zubair | |
---|---|---|
dc.contributor.author | Sadeghi, Parastoo | |
dc.contributor.author | Kennedy, Rodney | |
dc.contributor.author | Durrani, Salman | |
dc.date.accessioned | 2015-12-10T23:13:30Z | |
dc.date.created | 2012 | |
dc.identifier.issn | 1053-587X | |
dc.identifier.uri | http://hdl.handle.net/1885/64449 | |
dc.description.abstract | This correspondence studies a spatially localized spectral transform for signals on the unit sphere, which we call spatially localized spherical harmonics transform (SLSHT). For a systematic treatment, we explicitly express the transform in terms of rotated versions of an azimuthally symmetric window function and introduce the spatio-spectral SLSHT distribution with a succinct matrix representation. We present guidelines for the choice of the window function in the SLSHT, based on the inherent tradeoff between the spatial and spectral resolution of different window functions from the perspective of the uncertainty principle. We demonstrate the use of an eigenfunction window, obtained from the Slepian concentration problem on the sphere, as a good choice for window function. As an illustration, we apply the transform to the topographic map of Mars, which can reveal spatially localized spectral contributions that were not obtainable from traditional spherical harmonics analysis. | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en_AU | |
dc.publisher | Institute of Electrical and Electronics Engineers (IEEE Inc) | |
dc.source | IEEE Transactions on Signal Processing | |
dc.subject | Keywords: Eigen function; Matrix representation; Spectral contribution; Spectral transform; Spherical harmonics; Topographic map; Uncertainty principles; Window functions; Eigenvalues and eigenfunctions; Harmonic analysis; Maps; Signal analysis; Spectrum analysis; Signal analysis; spectral analysis; spheres; spherical harmonics | |
dc.title | Spatio-spectral Analysis on the Sphere Using Spatially Localized Spherical Harmonics Transform | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 60 | |
local.identifier.absfor | 090609 - Signal Processing | |
local.identifier.ariespublication | u4334215xPUB940 | |
local.type.status | Published Version | |
local.contributor.affiliation | Khalid, Zubair, College of Engineering and Computer Science, ANU | |
local.contributor.affiliation | Durrani, Salman, College of Engineering and Computer Science, ANU | |
local.contributor.affiliation | Sadeghi, Parastoo, College of Engineering and Computer Science, ANU | |
local.contributor.affiliation | Kennedy, Rodney, College of Engineering and Computer Science, ANU | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.issue | 3 | |
local.bibliographicCitation.startpage | 42156 | |
local.identifier.doi | 10.1109/TSP.2011.2177265 | |
local.identifier.absseo | 970109 - Expanding Knowledge in Engineering | |
dc.date.updated | 2016-02-24T11:04:34Z | |
local.identifier.scopusID | 2-s2.0-84857227981 | |
local.identifier.thomsonID | 000300424500044 | |
Collections | ANU Research Publications |
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02_Khalid_Spatio-spectral_Analysis_on_2012.pdf | 663.14 kB | Adobe PDF | Request a copy |
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