voigtian
Introduced in 2.0
Synopsis

Voigtian line shape.

y = voigtian(x,x0,fwhm)
y = voigtian(x,x0,fwhm,deriv)
Description

This function returns a Voigtian line shape with centre x0 and full width at half height fwhm over the abscissa values defined in the vector x. A Voigtian line shape is the convolution of a Gaussian and Lorentzian. fwhm specifies the full width at half height for both convolution components fwhm = [fwhmGauss fwhmLorentz].

deriv determines the derivative to compute. 0 stands for 0th derivative, 1 is the first one, 2 the second one, -1 indicates the integral with [eqn] as lower limit. If deriv is not given, it defaults to 0.

For long x vectors, the convolution takes time. If the performance is critical, pseudo-Voigt line shapes (linear combination of Gaussian and Lorentzian) can be computed with the function lshape.

Examples

To obtain a Voigtian with centre at 350 mT and FWHM of 20 mT for both Gaussian and Lorentzian, use

x0 = 350; x = x0+100*linspace(-1,1,1e3);
y = gaussian(x,x0,[20 20]);
plot(x,y);

The Voigtian is normalised, its integral is one.

sum(y)*(x(2)-x(1))
ans =
    1.0000
See also

convspec, gaussian, lorentzian, lshape