What is the formula for calculating the FWHM of a gaussian function?

In summary, The FWHM (Full Width at Half Maximum) of a Gaussian function is a measure of the width of the curve at half its maximum height. It represents the distance between the two points on the curve where the height is exactly half of the maximum value. The FWHM of a Gaussian function can be calculated using the formula FWHM = 2√(2ln2)σ, where σ is the standard deviation of the Gaussian distribution. Alternatively, it can also be calculated as 2.3548σ, where σ is the standard deviation. The FWHM of a Gaussian function provides information about the spread or width of the distribution. A larger FWHM indicates a wider distribution, while a smaller F
  • #1
peterjaybee
62
0
Hi,

I have a gaussian of the form
[tex]exp[-\frac{\pi*x^{2}}{A^2}][/tex].

I know that the FWHM=0.939A, but I cannot prove it.

I Let [tex]exp[-\frac{\pi*x^{2}}{A^2}=0.5[/tex] (i.e. the half maximum part)

taking natural logs I get rid of the exponential, but then which bit represents the full width?
 
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  • #2
Write x = kA and compute k=(-ln(.5)/π)1/2

Your Gaussian looks funny.
 

What is the FWHM of a Gaussian function?

The FWHM (Full Width at Half Maximum) of a Gaussian function is a measure of the width of the curve at half its maximum height. It represents the distance between the two points on the curve where the height is exactly half of the maximum value.

How is the FWHM of a Gaussian function calculated?

The FWHM of a Gaussian function can be calculated using the formula FWHM = 2√(2ln2)σ, where σ is the standard deviation of the Gaussian distribution. Alternatively, it can also be calculated as 2.3548σ, where σ is the standard deviation.

What does the FWHM of a Gaussian function tell us about the distribution?

The FWHM of a Gaussian function provides information about the spread or width of the distribution. A larger FWHM indicates a wider distribution, while a smaller FWHM indicates a narrower distribution.

How is the FWHM of a Gaussian function related to the standard deviation?

The FWHM of a Gaussian function is directly proportional to the standard deviation. This means that as the standard deviation increases, the FWHM also increases, and vice versa.

Why is the FWHM of a Gaussian function important in scientific research?

The FWHM of a Gaussian function is an important parameter in many scientific studies, especially in fields such as spectroscopy, signal processing, and image analysis. It can provide valuable information about the shape and characteristics of a distribution, and is often used to compare and analyze different data sets.

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