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