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

xndarray

Array of values at which to evalutate distribution.

x0float

Center of the distribution

sigmafloat

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

gammafloat

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

Returns

fndarray

Distribution evaluated at points in x.