S1FunHarmonic.S1FunHarmonic edit page

a class representing a function on the circle by its Fourier series

The function is stored by its Fourier coefficients fhat, running from degree -N to N. Accordingly fhat has an odd number of rows.

Syntax

sF = S1FunHarmonic(fhat)
sF = S1FunHarmonic(fun)
sF = S1FunHarmonic(fun,'bandwidth',N)

Input

`fhat`	`Fourier coefficients, from degree -N to N`
`fun`	`S1Fun or @function_handle to be approximated`

Output

`sF`	`S1FunHarmonic`

Options

bandwidth maximum harmonic degree

Class Properties

`fhat`	`Fourier coefficients`
`bandwidth`	`maximum harmonic degree`
`antipodal`	`f(x) = f(x + pi)`
`even`	`f(x) = f(-x)`
`odd`	`f(x) = -f(-x)`
`isReal`	`the function takes only real values`

Example

sF = S1FunHarmonic.quadrature(@(x) sin(2*x))

sF = S1FunHarmonic
  bandwidth: 1024
  antipodal: true
  odd: true

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/S1FunHarmonic.S1FunHarmonic.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.

S1FunHarmonic.S1FunHarmonic