the n-th de la Vallee Poussin kernel on the circle, 2 F_(2n-1) - F_(n-1) with F the Fejer kernels: coefficients one up to n, falling to zero at 2n

Syntax

S1DeLaValleePoussinKernel(20)
S1DeLaValleePoussinKernel(halfwidth=5*degree)

Description

A circular kernel with Fourier multipliers equal to one through degree n and falling linearly to zero at 2*n. The series is finite and has mean one. The halfwidth option chooses an integer n approximately, so the requested width is not exact.

Evaluate psi at x, an angle in radians. 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`		positive integer controlling the cutoff at 2*n; omitted n is chosen for about 2.9 degrees
`halfwidth`		approximate angular halfwidth in radians, used when n is omitted

Output

psi S1DeLaValleePoussinKernel

Members

bandwidth

the degree 2n beyond which the coefficients vanish

Used on

EllipseBasedParameters

MATLAB’s S1DeLaValleePoussinKernel

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/S1DeLaValleePoussinKernel_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 S1DeLaValleePoussinKernel