SLEPIAN Alpha

Computation of spherical harmonics, Slepian functions, and transforms

bandlimited functioncommuting differential operatorconcentration problemeigenvalue problemmultitaper spectral analysisspherical harmonics Read More: https://epubs.sia

true

Contributor(s)

Initial contribute: 2021-09-07

Authorship

:  
Princeton University
:  
fjsimons@gmail.com
Is authorship not correct? Feed back

Classification(s)

Method-focused categoriesProcess-perspectivePhysical process calculation

Detailed Description

English {{currentDetailLanguage}} English

Quoted from: https://epubs.siam.org/doi/10.1137/S0036144504445765

We pose and solve the analogue of Slepian's time-frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the sphere or, alternatively, of strictly spacelimited functions that are optimally concentrated in the spherical harmonic domain. Such a basis of simultaneously spatially and spectrally concentrated functions should be a useful data analysis and representation tool in a variety of geophysical and planetary applications, as well as in medical imaging, computer science, cosmology, and numerical analysis. The spherical Slepian functions can be found by solving either an algebraic eigenvalue problem in the spectral domain or a Fredholm integral equation in the spatial domain. The associated eigenvalues are a measure of the spatiospectral concentration. When the concentration region is an axisymmetric polar cap, the spatiospectral projection operator commutes with a Sturm--Liouville operator; this enables the eigenfunctions to be computed extremely accurately and efficiently, even when their area-bandwidth product, or Shannon number, is large. In the asymptotic limit of a small spatial region and a large spherical harmonic bandwidth, the spherical concentration problem reduces to its planar equivalent, which exhibits self-similarity when the Shannon number is kept invariant.

{{htmlJSON.HowtoCite}}

Frederik Simons (2021). SLEPIAN Alpha, Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/15eaf7e0-4354-4eb5-b375-2b584f525f29
{{htmlJSON.Copy}}

Contributor(s)

Initial contribute : 2021-09-07

{{htmlJSON.CoContributor}}

Authorship

:  
Princeton University
:  
fjsimons@gmail.com
Is authorship not correct? Feed back

History

Last modifier
Wenfei Shen
Last modify time
2021-09-18
Modify times
View History

QR Code

×

{{curRelation.overview}}
{{curRelation.author.join('; ')}}
{{curRelation.journal}}









{{htmlJSON.RelatedItems}}

{{htmlJSON.LinkResourceFromRepositoryOrCreate}}{{htmlJSON.create}}.

Drop the file here, orclick to upload.
Select From My Space
+ add

{{htmlJSON.authorshipSubmitted}}

Cancel Submit
{{htmlJSON.Cancel}} {{htmlJSON.Submit}}
{{htmlJSON.Localizations}} + {{htmlJSON.Add}}
{{ item.label }} {{ item.value }}
{{htmlJSON.ModelName}}:
{{htmlJSON.Cancel}} {{htmlJSON.Submit}}
Name:
Version:
Model Type:
Model Domain:
Scale:
Purpose:
Principles:
Incorporated models:

Model part of

larger framework

Process:
Information:
Initialization:
Hardware Requirements:
Software Requirements:
Inputs:
Outputs:
{{htmlJSON.Cancel}} {{htmlJSON.Submit}}
Title Author Date Journal Volume(Issue) Pages Links Doi Operation
{{htmlJSON.Cancel}} {{htmlJSON.Submit}}
{{htmlJSON.Add}} {{htmlJSON.Cancel}}

{{articleUploading.title}}

Authors:  {{articleUploading.authors[0]}}, {{articleUploading.authors[1]}}, {{articleUploading.authors[2]}}, et al.

Journal:   {{articleUploading.journal}}

Date:   {{articleUploading.date}}

Page range:   {{articleUploading.pageRange}}

Link:   {{articleUploading.link}}

DOI:   {{articleUploading.doi}}

Yes, this is it Cancel

The article {{articleUploading.title}} has been uploaded yet.

OK
{{htmlJSON.Cancel}} {{htmlJSON.Confirm}}