an even kernel on the circle represented by a finite Fourier series.

Syntax

psi = S1Kernel(fhat)
values = psi(angles)

Description

Input coefficients are ordered from mode -N to N and are expected to be real and even: c[-k]=c[k]. The constructor stores the nonnegative half and mirrors it on output. Angles are in radians, with period 2*pi. The middle coefficient is the mean over the circle; choose it as one for a mean-one smoothing kernel.

Input

fhat real symmetric coefficient array of odd length 2*N+1

Output

psi S1Kernel

Properties

`fhat`	two-sided coefficients, modes -N through N
`bandwidth`	largest Fourier mode N

Members

calcFourier	the Fourier coefficients of the kernel, degrees -L .
conv	the convolution with another kernel on the circle: the coefficients multiplied
grad	the derivative of a kernel on the circle, -2 sum_k k c_k sin(kx)
norm	the L2 norm of the kernel, the Euclidean norm of its two sided coefficients

MATLAB’s S1Kernel_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/S1Kernel_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.

The class S1Kernel