the indicator of the interval x < delta scaled to a density

Syntax

psi = S1BumpKernel()

Description

A periodic constant kernel on the open interval (-delta, delta), with zero values outside. The height is pi/delta, giving mean one over the circle. Its derivative is zero away from the two discontinuities and is undefined at them.

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
delta   angular radius of the open support in radians
halfwidth   angular halfwidth in radians, taking precedence over delta

Output

psi S1BumpKernel

See also

S1Kernel, calcDensity, calcKernel

Members

grad the derivative of the bump kernel, zero wherever it exists
halfwidth the halfwidth, the half length delta of the interval

MATLAB’s S1BumpKernel_index

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/S1BumpKernel_index_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.