the Dirichlet kernel on the sphere, sum_n (2n+1) P_n(t) up to the degree N, of mean one

Syntax

S2DirichletKernel(35)

S2DirichletKernel()

N the preference maxS2Bandwidth.

Description

Convolution with this kernel retains spherical harmonic degrees 0 through N unchanged and removes higher degrees. It has mean one but can take negative values; nonnegative smoothing kernels are usually preferable for density estimation.

Evaluate psi at t=cos(theta), the cosine of the angular distance on the sphere. Use psi.halfwidth() for the angular width in radians and psi.bandwidth for the maximum degree of its harmonic representation.

Keywords

keyword	default	description
`N`		maximum harmonic degree; the maxS2Bandwidth preference when omitted

Output

psi S2DirichletKernel

Members

bandwidth

the degree N of the kernel

Used on

S2Kernels, VectorsDensityEstimation

MATLAB’s S2DirichletKernel

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/S2DirichletKernel_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.

The class S2DirichletKernel