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