the Fourier coefficients c_{-L} .. c_L from weighted values at the angles x, the sum of w v e^{-ikx}; a quadrature grid brings the weights of its rule

Syntax

chat = fourierSeriesAdjoint(x, np.cos(x), 1)

The weights 1/n.

chat = fourierSeriesAdjoint(x, np.cos(x), 1, weights=w)

Weighted.

chat = fourierSeriesAdjoint(quadratureS1Grid(16), values, 8)

The quadrature of a grid.

Description

The adjoint of fourierSeries, directly or by the NUFFT; at equispaced angles with weights 1/n the coefficients of a trigonometric polynomial of degree L.

Input

x the angles, or a quadratureS1Grid
values the values at the angles
L the bandwidth

Keywords

keyword default description
weights None the weight of every angle; by default 1/n, or the grid’s rule

Output

chat the 2L+1 coefficients, complex

See also

fourierSeries, 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/fourierSeriesAdjoint_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.