how to do convolution of a finite data series with gaussian

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Wed, 12/10/2014 - 03:01 pm

Hi, I am new to Igor and I need to do convolution of a finite series of X,Y data with a Gaussian. after that I want to see if this data fits in my experimental peak.
I am expecting to get an asymmetric peak after convolution
My plan is to choose a series of data which fits my experimental peaks better but I don't want to go through fitting now not to make it complicated
I have gone through the help but it was about convolution of two function and not a data series. I have attached the data as well.
Thanks in advance question from Igor.pxp
I don't get what you want to do, but if you want to convolve data then the Convolve function is your friend. Duplicate one of your data waves and fill it with a Gaussian of your liking via the Gauss function. Then use Convolve to blend this peak with your data. It can of course also be done on the fly in a fitting function (which might be a bit fiddly to do).

December 10, 2014 at 04:57 pm - Permalink

Hi again and thanks for your reply I will check to see if I am able to use your suggestion.
To explain in more details: According to my experiment, I have an asymmetrical peak and I want to use the theory that is explaining this asymmetry. I want to see if this theory is in agreement to my experimental data. The theory that I used has given me a finite data series which does not have a peak-like shape but I think if I convolve it with a Gaussian it will get the shape of a peak. And If I want to compare this theory with experimental result I think I should do fitting while convolution.
My problem is that I don't know how to do fitting while convolution of a data series with a Gaussian.

Thanks again

December 11, 2014 at 05:27 pm - Permalink

A delta-function convolved with any shape is that shape. A delta-function convolved with a Gaussian peak is a Gaussian peak. Suppose your Gaussian peak has a FWHM of 1 (in whatever units). When you have two delta functions that are spaced by a distance of 1 or less apart, and you convolve that "spectrum" with a single Gaussian, you will get an overlapping set of peaks. The overlapping peaks can be "deconvolved" by peak fitting with two Gaussian peaks, each having the same FWHM (1).

I wonder if you are facing a simpler peak fitting problem rather than peak deconvolution problem?

--
J. J. Weimer
Chemistry / Chemical & Materials Engineering, UAHuntsville

December 12, 2014 at 10:07 am - Permalink

I'm going to shamelessly plug my own project called "Linebroadening", because I think it's exactly what you're looking for.

http://www.igorexchange.com/project/LineBroadening

As chozo and jjweimer noted, there is a built-in "convolve" operation in Igor, but it only works if adding an extra broadening effect to data that is already in equally spaced x-increments. It sounds like you're trying to take a theoretical prediction of line data (like spectral data in the form intensity vs. wavelength or intensity vs. frequency) that you cannot resolve on your instrument. When you say you expect an "asymmetric peak" you mean you don't expect it to represent one pure transition, right but a combination of a bunch of unresolved lines that are asymmetrically distributed, right?

Basically, the link I pointed you has functions to scale the convolution so that it pays attention to the x-spacing in waveform data (and if you're new to Igor, you should read up on how to work with waveform data) and also to convert X,Y line data to unbroadened waveform data that can be convolved with a lineshape function.

As for running a least-squares fit...it can be done with all-at-once fitting, but if you're trying to explain an asymmetric peak shape by using intensity,frequency pairs that are not adjusted as part of the fit, you're going to find that your peak shape is very insensitive to the width of the Gaussian function once the width is high enough that you cannot resolve the lines, and therefore the fit will give you a large uncertainty or just fail to converge.

-Ian

December 20, 2014 at 05:26 am - Permalink