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 Gaussian-Lorentzian Cross Product Function?
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Punix

2 Posts

Posted - 09/10/2013 :  07:47:50 AM  Show Profile  Edit Topic  Reply with Quote  View user's IP address  Delete Topic
Origin Ver. and Service Release (Select Help-->About Origin): OriginPro 8 SR4
Operating System: Windows 7

I have the following problem:
If I check the function that Origin uses for GL Cross product function (http://www.originlab.com/www/helponline/origin/en/UserGuide/Gaussian_LorenCross.html) I wonder about a little more information. So far i found out that the width in there is only the HWHM. Which is very confusing because in related Lorentzian and Gaussian functions it is the FWHM. Also there should be at least two possibilites to form a cross product (based on amplitude or based on integral) which one was used to create this function?

I was also wondering if the shape parameter 1 still resembles a full Lorntzian function because if i compare it to the Lorentzian function i do not find the same omega dependency.

Whats the trick here?

Thank you very much already in advance

EDIT: http://www.originlab.com/forum/topic.asp?TOPIC_ID=5254
this topic does not help me at all since it only states something about the pseudo voigt functions but not about my question about the cross product function

Edited by - Punix on 09/10/2013 07:51:31 AM

Sam Fang

293 Posts

Posted - 09/13/2013 :  03:10:39 AM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
1. w in Gaussian_LorenCross is a half width at which the y value is equal to 1/(1+exp(0.5*(1-s))*s) of its maximum value. Note that when s=1 (Lorentz), it is half of FWHM.

2. Amplitude is used here, and A is the amplitude.

3. If s=1, it converts to Lorentz function. w is half of FWHM in Lorentz, and A is 2*Area/(pi*FWHM) in Lorentz.

Sam
OriginLab Technical Services
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