S2FunHarmonic.evalEquispacedFFT edit page

Evaluate an S2FunHarmonic on an equispaced grid in spherical coordinates \[(\theta_a,\rho_b) = (\frac{\pi a}{Htheta-1},\frac{2\pi b}{Hrho})\] where \(a=0,...,Htheta-1\) and \(b=0,...,Hrho-1\).

Therefore we transform the Harmonic series to an ordinary Fourier series equivalent as in the function eval. Afterwards, we use an equispaced FFT instead of the NFFT.

Syntax

f = evalEquispacedFFT(sF,v)

Input

sF S2FunHarmonic
v quadratureS2Grid - 'ClenshawCurtis'

Output

f values at this grid points

Example

construct quadrature grid and evaluate there. Output will be a unique part of this grid

sF = S2FunHarmonic.smiley;
v = quadratureS2Grid(100,'ClenshawCurtis');
f = evalEquispacedFFT(sF,v);

for big grid sizes the construction of the quadrature grid is memory expansive. Hence construct a struct, but the output is full sized

v = struct('scheme','ClenshawCurtis','bandwidth',1500)
f = evalEquispacedFFT(sF,v);
v = 
  struct with fields:

       scheme: 'ClenshawCurtis'
    bandwidth: 1500

See also

S2FunHarmonic.eval S2FunHarmonic.evalNFSFT

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/S2FunHarmonic.evalEquispacedFFT.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.