Hilbert transform.

y_h = hilberttrans(y)

This function computes the Hilbert transform of input vector y and returns it in y_h.

More precisely, y_h actually computes the analytical signal from y. The real part of y_h contains the original signal y, whereas the imaginary part of y_h contains the Hilbert transform.

To obtain the dispersion of a Gaussian line shape from the absorption form, use

x0 = 0; w = 0.1;
x = linspace(-1,1,1000)*3;
yabs = gaussian(x,x0,w);
ydisp = hilberttrans(yabs);
ydisp = imag(ydisp);
plot(x,yabs,x,ydisp);

You can compare this to the dispersion that's directly provided by gaussian,

[yabs,ydisp0] = gaussian(x,x0,w);
plot(x,ydisp,x,ydisp0);

convspec, gaussian, lorentzian, lshape, voigtian