How can I create a Gaussian curve with given data?

[csand]

Hi,
My understanding in this is limited, but I'm trying to create a set of Gaussian curve response functions that will be convoluted with some signal data. I've dug all around the internet/textbooks but I'm having trouble finding a way to create the curve with the data I have. All I know is the height is bound from 0 to 1 (or at least very very close to 0 for my purposes). I have the center value (x-axis) for every curve I need to generate, and I know the FWHM of every curve. So to generate a curve I will know:

-FWHM for the curve
-The center xaxis value (Denoted by Lambda_Center)
-The height

The only formula I have is unsourced and I'm not sure it's working properly for all cases:

e^( -1*(Lambda - Lambda_Center)^2 / (FWHM/2*sqrt(ln2))^2 )

I have Lambda_Center, and Lambda, if this were to be looped in a program, would increment/decrement by some value X for each point on the gaussian (ex: 0.1,0.2,0.3,0.4,L_C,0.4,0.3,0.2,0.1)

Does anyone recognize this formula/method for creating a gaussian? Can anybody see any big holes in the method? Everything I see online usually involves using sigma/mean.

Thanks,
-Chris

***EDIT***: fixed formula bracketing

 

[pmsrw3]

e^[ -1*(Lambda - Lambda_Center)^2 / (FWHM]/2*sqrt(ln2))^2) ]

Looks right, except that you have some issues with parens and brackets. But look, there's an easy way to test it. You want the value to be 1 at Lambda_Center and 0.5 at Lambda_Center +- FWHM. So plug in those numbers and see if it works.

 

[csand]

I have created some curve data with this formula, and for the most part the data seems reasonable. However, I find that sometimes I need hundreds of points just to see the function approach 0, and, unless I choose a very high resolution step (such as 0.01), I don't often find a 0.5, but values close to, such as 0.52xxxx,0.489xxxx, etc. I'm glad to know that the formula, other than the bracketing errors, appears legitimate.

Thanks,
-C

 

[pmsrw3]

I'm not sure how closely you need it to get down to zero. It will get to 0.05 at 2.08 FWHM, to 0.01 at 2.58 FWHM, and 0.001 at 3.16 FWHM. Obviously, if your points are spaced such that FWHM is 100 of them, it's going to take hundreds of points to get down near zero. (I assume they're equally spaced.) Nothing to do about that.

You should not expect to get exactly 0.5 at any of your points unless the spacing of the points exactly divides FWHM and Lambda_Center exactly corresponds to one of the points.

I was not actually suggesting that you look at the points generates by your program. I was suggesting that YOU actually plug the numbers into the formula YOURSELF and check that it gives the right result.

EDIT: Oops! I just realized that, while I've been writing FWHM, I was actually thinking HWHM. So everything I've said so far is off by a factor of two. If you replace FWHM with FWHM/2 in the above, then it should be right.

 

[blue_raver22]

Hello Chris,

Creating a Gaussian curve with given data can be done using the formula you have provided, which is the standard Gaussian probability density function. This formula is commonly used in statistics and probability to represent a normal distribution.

To ensure that the formula is working properly for all cases, it is important to understand the parameters involved. The FWHM (full width at half maximum) determines the width of the curve, while the Lambda_Center represents the mean or center value of the curve. The height of the curve will depend on the maximum value of your data.

In order to create a curve for each data point, you can use a loop in your program to increment or decrement the Lambda value by a fixed interval (X) as you have mentioned. This will generate a curve for each data point with the given FWHM and Lambda_Center values.

It is worth noting that the use of sigma and mean is another way to represent the FWHM and Lambda_Center values. They are related by the formula FWHM = 2*sqrt(2*ln2)*sigma, where sigma is the standard deviation and mean is the average of your data.

Overall, your method for creating a Gaussian curve with given data seems valid. However, it is always recommended to test the results and compare them with known Gaussian curves to ensure accuracy. Additionally, you can also explore other methods and algorithms for generating Gaussian curves, such as the Box-Muller transform or the Metropolis-Hastings algorithm.

I hope this helps. Best of luck with your project.

Sincerely,