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slepians.jl

Numerical solution to the optimization problem of constraining spatially a function and its Fourier transform.

https://github.com/lootie/slepians.jl

Science Score: 44.0%

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Keywords

fourier-transform
Last synced: 8 months ago · JSON representation ·

Repository

Numerical solution to the optimization problem of constraining spatially a function and its Fourier transform.

Basic Info
  • Host: GitHub
  • Owner: lootie
  • License: other
  • Language: TeX
  • Default Branch: master
  • Homepage:
  • Size: 46.3 MB
Statistics
  • Stars: 4
  • Watchers: 1
  • Forks: 2
  • Open Issues: 0
  • Releases: 1
Topics
fourier-transform
Created over 4 years ago · Last pushed over 1 year ago
Metadata Files
Readme License Citation

README.md

Slepians.jl

Slepians.jl is a package that solves the concentration problem of Slepian, Landau and Pollak, numerically. Loosely speaking, we find a function that is both finite in extent, and has a Fourier transform which lies in a certain domain. In a single dimension, with discrete sampling, the discrete prolate spheroidal sequences solve this optimization problem.

Installation

Slepians.jl is unregistered and relies on unregistered packages. To avoid difficulties in which Julia does not know the relevant URLS, I have created a registry bbkt-reg.jl which will tell your installation where to find this package and its dependencies. Begin with adding the registry using

pkg> registry add https://github.com/lootie/bbkt-reg.jl

then one can simply add the Slepians.jl package as

pkg> add Slepians

Examples

The jupyter notebooks in the Examples/ directory illustrate the functionality of this package.

Funding

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Materials Science and Engineering.

References

Please see the below papers

``` @article{bronez1988spectral, title={Spectral estimation of irregularly sampled multidimensional processes by generalized prolate spheroidal sequences}, author={Bronez, Thomas P}, journal={IEEE Transactions on Acoustics, Speech, and Signal Processing}, volume={36}, number={12}, pages={1862--1873}, year={1988}, publisher={IEEE} }

@article{slepian1978prolate, title={Prolate spheroidal wave functions, Fourier analysis, and uncertainty—V: The discrete case}, author={Slepian, David}, journal={Bell System Technical Journal}, volume={57}, number={5}, pages={1371--1430}, year={1978}, publisher={Wiley Online Library} }

@article{simons2011spatiospectral, title={Spatiospectral concentration in the Cartesian plane}, author={Simons, Frederik J and Wang, Dong V}, journal={GEM-International Journal on Geomathematics}, volume={2}, number={1}, pages={1--36}, year={2011}, publisher={Springer} } ```

Owner

  • Name: C. L. Haley
  • Login: lootie
  • Kind: user
  • Location: Lemont, IL
  • Company: Argonne National Laboratory

I am interested in signal processing, spectral analysis of time series and spatial statistics.

Citation (CITATION.cff) 

cff-version: 0.1.0
message: "If you use this software, please cite it as below."
authors:
- family-names: "Haley"
  given-names: "Charlotte"
  orcid: "https://orcid.org/0000-0003-3996-773X"
title: "Slepians.jl"
version: 2.0.4
date-released: 2021-09-29
url: "https://github.com/lootie/Slepians.jl"

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