Gaussian, Lorentzian and pseudo-Voigt line shapes.

y = lshape(x,x0,fwhm)
y = lshape(x,x0,fwhm,diff)
y = lshape(x,x0,fwhm,diff,alpha)
y = lshape(x,x0,fwhm,diff,alpha,phase)

lshape evaluates normalised line shapes over a given abscissa vector x. x0 is the centre of the line shape, fwhm denotes the line shape's full width at half height (FWHM).

If diff is given, it specifies the derivative wanted: 1 for first and 2 for second derivative. 0 means no derivative, which is the default. -1 indicates the integral with as lower limit.

If alpha is given, it determines the line shape function. alpha = 1 is a pure Gaussian (the default), and alpha = 0 a pure Lorentzian. Any value in between gives a hybrid pseudo-Voigt function

For the pseudo-Voigt function either one or two widths can be specified. If fwhm is a scalar, it is used for both components, if it is a 2-element vector, the first element gives the line width for the Gaussian and the second that for the Lorentzian component.

phase determines the phase of the Lorentzian component. 0 is pure absorption, and pi/2 is pure dispersion.

The code

x = -100:100; centre = -30;
y = lshape(x,-30,20,1,0);
plot(x,y)

produces a plot of the first derivative of a Lorentzian, a very common line shape in CW EPR spectroscopy.

For the mathematical expressions for the various line shapes, see gaussian and lorentzian.

convspec, gaussian, hilberttrans, lorentzian, voigtian