# Understanding the Difference Between Gaussian Functions

• nordmoon
In summary, the Gaussian function is a probability distribution with a flat power spectral density. The Gaussian noise is properly defined as having a Gaussian amplitude distribution, but this does not describe its correlation in time or spectral density. The Gaussian function can be used to represent the line profile of a spectral line in a spectrum of light, and can be used in conjunction with other functions to obtain more complex line profiles.

#### nordmoon

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

Does anyone have a clue?

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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."

chingkui said:
HallsofIvy said:
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 reffering 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?

## 1. What is a Gaussian function?

A Gaussian function, also known as a Gaussian distribution or a normal distribution, is a mathematical function that describes the shape of a bell curve. It is commonly used in statistics and data analysis to model continuous data that is symmetric around a mean value.

## 2. How is a Gaussian function different from other types of functions?

A Gaussian function is characterized by its bell-shaped curve, which is symmetrical around its mean value. This means that the data is equally distributed on either side of the mean. Other types of functions may have different shapes and distributions, such as exponential or logarithmic functions.

## 3. What are the key features of a Gaussian function?

The key features of a Gaussian function include its mean, standard deviation, and maximum value. The mean represents the center of the bell curve, while the standard deviation controls the spread of the data around the mean. The maximum value is the highest point on the curve, which occurs at the mean.

## 4. How is a Gaussian function used in real-world applications?

Gaussian functions are used in a variety of real-world applications, including finance, engineering, and natural sciences. They are commonly used to model data in fields such as economics, physics, and astronomy. They can also be used in image processing and pattern recognition algorithms.

## 5. What is the relationship between a Gaussian function and the normal distribution?

The terms "Gaussian function" and "normal distribution" are often used interchangeably because they refer to the same mathematical concept. A normal distribution is a probability distribution that follows a Gaussian function. This means that the data follows a bell-shaped curve and is symmetrically distributed around the mean.

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