# Data convolution

1. Mar 16, 2015

### Kartik82

Hi, Can any one please help me in convoluting atomic data. Along x-axis I have wavelenght and on Y axis I have scattered intensity. I want to convolute with FWHM of 20mm.
Thanks
Kartik

2. Mar 17, 2015

### Quantum Defect

3. Mar 17, 2015

### Kartik82

Hi,
Thanks for your reply. Its Gaussian profile. As an example please see the attached one data set that I want to convolute.

#### Attached Files:

• ###### Data.xlsx
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4. Mar 18, 2015

### Quantum Defect

X and Y are what?

5. Mar 18, 2015

### Kartik82

Hi, X-axis is wavelength and y-axis is intensity.
Best regards,
Kartik

6. Mar 18, 2015

### Quantum Defect

First thing generally is to sort the transitions by wavelength/frequency however you want to do things.
You can do this in excel, but it is more efficient to write a program to do this.

If you do this in excel, you want to create a set of x values that are uniformly spaced, with a point density that is good enough to give you a smoothness that you can live with. I.e. 3 points over your FWHM is probably too coarse, but 3,000 is way to many. You decide. Populate a column vector with these values.

You can create the spectrum of Gaussian lines in a variety of ways. The simplest (but computationally inefficient way) is to add up all of the contributions for all of the lines at each X grid point.

e.g. if x = 8.0000, y = SUM(Intensity_i*(exp[-(8.0000-x_i)^2/sigma] ) Where "Intensity_i" are your y-values in your original spreadsheet, the "x_i" are the x values in your original spreadsheet, and sigma is obtained from the Gaussian that you are assuming. If the different transitions have different effective Gaussian widths, you could have a third column in your original spreadsheet. In excel, you may get a floating point error if you are too far away from the line (i.e. if x is too far away from x_i), in which case you may have to play with the limits of the sum. In a program, you could fix these with something that checks to see if x is more than 4 sigma away from the xi, and not bother to calculate the intensity if the line falls outside of this range.

7. Mar 19, 2015

### Kartik82

Hi,
Thank you so much for the detailed explanation. I will work on this and will let you know how it goes.
Best regards,
Kartik