the Dirichlet kernel on the circle, sum_(k = -n .. n) e^(ikx), of mean one

Syntax

psi = S1DirichletKernel()

Description

The sharp Fourier cutoff: convolution retains modes -n through n unchanged and removes the rest. The mean over the circle is one. Oscillating negative side lobes can produce ringing when approximating discontinuous data.

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   maximum harmonic degree

Output

psi S1DirichletKernel

See also

S1Kernel, calcDensity, calcKernel

Members

bandwidth the degree n of the kernel

MATLAB’s S1DirichletKernel_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/S1DirichletKernel_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.