the Fourier series sum of chat_k e^{ikx} at the angles x, directly or by NUFFT; real when the coefficients are those of a real function

Syntax

y = fourierSeries([0.5, 1, 0.5], np.linspace(0, 2*np.pi, 50))

1 + cos(x).

y = fourierSeries([0.5, 1, 0.5], x, real=False)

The complex values.

y = fourierSeries(chat, quadratureS1Grid(16))

At the nodes of a grid.

Description

The coefficients are c_{-L} .. c_L over e^{ikx}, the internal ones of an S1FunHarmonic (MATLAB’s fhat runs over e^{-ikx}). The result has the shape of x.

Input

chat the 2L+1 coefficients
x the angles, or a quadratureS1Grid

Keywords

keyword default description
real None whether the coefficients are those of a real function, whose values are returned real; by default isRealFourier(chat)

Output

y the values, real for real coefficients

See also

fourierSeriesAdjoint, S1FunHarmonic

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/fourierSeries_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.