Voigtian line shape (absorption and dispersion).

ya = voigtian(x,x0,fwhmGL)
ya = voigtian(x,x0,fwhmGL,diff)
ya = voigtian(x,x0,fwhmGL,diff,phase)
[ya,yd] = voigtian(...)

This function returns a Voigtian line shape with center x0 and component full widths at half height fwhmGL over the abscissa values defined in the vector x. A Voigtian line shape is the convolution of a Gaussian and Lorentzian line shape.

fwhmGL specifies the full width at half height for the two convolution components fwhmGL = [fwhmGauss fwhmLorentz]. If both are non-zero, a Voigtian line shape results. There are two limiting cases: If the first element in fwhmGL is zero, you get a pure Lorentzian. If the second element is zero, you get a pure Gaussian.

diff determines the derivative to compute. 0 stands for no derivative, 1 is the first one, 2 the second one, and so on. -1 indicates the integral with as lower limit. If diff is not given, it defaults to 0.

The function returns the absorption line shape in ya and the 90-degree phase-shifted dispersion line shape in yd.

If phase is given, the absorption and dispersion line shapes are both rotated the by the given amount (in radians). E.g., with phase=pi/2, ya will contain the dispersion line shape.

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.

To obtain a Voigtian with center at 350 mT, a Gaussian FWHM of 2 mT, and a Lorentzian FWHM of 1 mT, use

x0 = 350;
x = x0+50*linspace(-1,1,1e3);
fwhmGL = [2 1];
y = voigtian(x,x0,fwhmGL);
plot(x,y);

The Voigtian is normalized, i.e. its integral is one.

sum(y)*(x(2)-x(1))

ans =
    0.9936

convspec, gaussian, hilberttrans, lorentzian, lshape