Understanding the Difference Between Gaussian Functions

[nordmoon]

I am having difficulty understanding the difference between the http://en.wikipedia.org/wiki/Gaussian_function" ? Which one would, say represent the line profile of a spectral line?

Does anyone have a clue?

 

[HallsofIvy]

The Gaussian function is a function, just like "sin(x)" or "ln(x)". The Gaussian distribution is probability distribution whose density function is the Gaussian function. As for the 'line profile of the spectral line' that appears to be an application I am not familiar with. Are you referring to an actual spectrum of light or the spectrum of a linear operator?

 

[chingkui]

I think nordmoon is referring to Gaussian White Noise.
If that's the case, then you can get some more info from Wikipedia.
I am quoting from Wikipedia:
http://en.wikipedia.org/wiki/White_noise
"White noise is a random signal (or process) with a flat power spectral density."
http://en.wikipedia.org/wiki/Gaussian_noise
"Gaussian noise is properly defined as the noise with a Gaussian amplitude distribution.
This says nothing of the correlation of the noise in time or of the spectral density of the noise. Labeling Gaussian noise as 'white' describes the correlation of the noise. It is necessary to use the term "white Gaussian noise" to be correct. Gaussian noise is sometimes misunderstood to be white Gaussian noise, but this is not the case."

 

[nordmoon]

The Gaussian function is a function, just like "sin(x)" or "ln(x)". The Gaussian distribution is probability distribution whose density function is the Gaussian function. As for the 'line profile of the spectral line' that appears to be an application I am not familiar with. Are you referring to an actual spectrum of light or the spectrum of a linear operator?

I think nordmoon is referring to Gaussian White Noise.
If that's the case, then you can get some more info from Wikipedia.
I am quoting from Wikipedia:
http://en.wikipedia.org/wiki/White_noise
"White noise is a random signal (or process) with a flat power spectral density."
http://en.wikipedia.org/wiki/Gaussian_noise
"Gaussian noise is properly defined as the noise with a Gaussian amplitude distribution.
This says nothing of the correlation of the noise in time or of the spectral density of the noise. Labeling Gaussian noise as 'white' describes the correlation of the noise. It is necessary to use the term "white Gaussian noise" to be correct. Gaussian noise is sometimes misunderstood to be white Gaussian noise, but this is not the case."

I am referring to the spectral line profile in a spectrum of light. Spectral lines can have a spectral line profile which is either a Voigt, Lorentzian or Gaussian profiles. I was looking for an equation which would plot the gaussian line profile in order to later obtain the Voigt line profile which is the convolution between the Lorentzian and the Gaussian profiles. My intension is to use these for spectral line fitting.

What I have is the peak maximum, the central line wavelength and the FWHM. Would one be able to apply the Gaussian function and say that it's the Gaussian line profile of that spectral line?