nmrglue.analysis.lineshapes1d.sim_voigt_sigmagamma

nmrglue.analysis.lineshapes1d.sim_voigt_sigmagamma(x, x0, sigma, gamma)

Simulate a Voigt lineshape with unit height at the center.

Simulates discrete points of the continuous Voigt profile with unit height at the center. Sigma and gamma are used as the Gaussian and Lorentzian scaler parameters.

Functional Form:

f(x; x0, sigma, gamma) = Re[w(z)] / Re[(w(z0)]

Where:

z = ((x - x0) + 1j * gamma) / (sigma * sqrt(2)) z0 = (1j * gamma) / (sigma * sqrt(2)) w(z) is the complex error function of z

Parameters :

x : ndarray

Array of values at which to evalutate distribution.

x0 : float

Center of the distribution

sigma : float

Gaussian scale component of Voigt profile. Variance of the Gaussian distribution.

gamma : float

Lorentzian scale component of Voigt profile. Half-width at half-maximum of the Lorentzian component.

Returns :

f : ndarray

Distribution evaluated at points in x.