a function on the circle by its Fourier coefficients fhat, k = -L..L, over e^{-ikx} as MATLAB’s

Syntax

sF = S1FunHarmonic([0.25, 0, 1, 0, 0.25])

From the coefficients, k = -2..2.

sF = S1FunHarmonic(lambda x: np.sin(2*x), bandwidth=16)

A callable by quadrature.

sF = S1FunHarmonic(psi, bandwidth=32)

The Fourier series of an S1 kernel.

sF = S1FunHarmonic(sF, bandwidth=8)

Another function, cut to a bandwidth.

Description

The coefficients run from the degree -L to L, so a coefficient vector has odd length 2 L + 1. A callable is sampled on the equispaced quadrature grid of the bandwidth, by default the preference maxS1Bandwidth; an S1 kernel, an S1FunHandle or another S1FunHarmonic gives its own coefficients, cut or padded to the bandwidth when one is given. A real function keeps c_{-k} = conj(c_k), which is checked from the coefficients unless real says it.

Input

fhat array of 2 L + 1 coefficients, a callable of the angle, an S1Kernel or an S1Fun

Keywords

keyword	default	description
`real`	`None`	whether the function takes real values only; by default read off the coefficients or the sampled values
`bandwidth`	`None`	the largest degree L of the series
`dtype`	`None`	the complex type of the coefficients, complex128 unless given

Output

`sF`	S1FunHarmonic

Properties

`fhat`	complex coefficients ordered from Fourier mode -L through L
`bandwidth`	largest Fourier mode L
`isReal`	whether the function is constrained to have real values
`antipodal`	whether f(x+pi)=f(x), read from its coefficients
`even, odd`	boolean symmetry tests under x -> -x

Used on

S1FunHarmonics

MATLAB’s S1Fun.S1Fun

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/S1Fun.S1Fun_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.

S1Fun.S1Fun