Peak fitting with constraints

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Wed, 10/14/2015 - 02:53 am

Hi all,

I have been playing around with some peak fitting lately....I have two peaks overlapping with each other and i have been trying to see what happens if i introduce constraints. So, i fix the position of one and check if the position of the other changes or not.....The case is that sometimes it does and sometimes it seems that by fixing the position of one within a certain waveumber range (6-7cm-1), the position of the second (not constrained one) remains fairly stable. I am trying to understand if there is any way to ''predict'' when this is likely to happen and what is the reason why sometimes the position of one peak affects the other as well or not. I thought that it is related to the ''degree of overlapping'', meaning that if the 2 peaks overlap much probably the position of one peak can affect the other one as well. However, i tried that process with different data sets and i saw that this is not the case. Could it be related to the width of the peaks? Is it the fact that the position of a narrow peak is more robust during fitting (meaning more stable) than a wide peak? Last but not least, is there a way to realise these changes when we have more than 2 peaks (e.g. 3 or 4)? Sorry for the massive text, if someone has any ideas please share.

My kindest regards,

Konstantinos
It is my experience that the more the two overlapping peaks can be described as just a single broader peak, the more uncertain the fit becomes, since multiple different combinations of areas, positions and widths start to fit the combined spectrum equally well. A change in area, position or width of peak 1 would then be compensated by a change in peak 2. I don't know if that is of any help to you.

October 14, 2015 at 07:33 am - Permalink

Hi,

Thanks for your reply.....I generally agree, i think that especially when you have more than 2 peaks things become unpredictable due to the fact that you can have multiple different combinations until the software comes up with the best chi square. However, i noticed that when you have 3 peaks where 2 of them are broad (say FWHM of 30) and the third is sharper (say FWHM 16-17) and you change the position of one broad peak, then the other broad peak is also affected but the sharp is more robust. To make long story short, i have the feeling that sharper peaks appear more stable in terms of position compared to broad ones. Maybe i am wrong and there is no real way of predicting this.....probably in another data set even sharper peaks are also affected.

October 14, 2015 at 07:59 am - Permalink

This thread is just a bit on the vague side...

If you can actually see bumps, then there is a clear signal to constrain the width and location of the peak.

It makes sense that a broad peak is not as well located as a narrow one. If you think about a normalized peak with width=1, then you will get a certain amount of misfit as the model peak slides sideways. That misfit will depend on the fraction of mis-location. Think of convolving a Gaussian with another Gaussian- the result is also Gaussian with a width that depends on the widths of the inputs.
Quote:
I thought that it is related to the ''degree of overlapping'', meaning that if the 2 peaks overlap much probably the position of one peak can affect the other one as well. However, i tried that process with different data sets and i saw that this is not the case.

It really does depend heavily on the degree of overlap. In my experience, as long as you can actually see a bump, you can fit it. Heavy overlap tends to look more and more like a single peak the closer they get, and when it looks to your eye like one peak, it probably affects the ability to fit.

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com

October 14, 2015 at 09:21 am - Permalink

Hi John,

Thanks for your input....I looked at one data set where i had two overlapping broad peaks....One of them was very intense and the other one not.....Changing the position of the small peak i could see that the big one was also affected. In another data set, i had one broad peak and a sharp peak again overlapping. The sharp peak was more intense and the degree of overlapping was higher than in the first case (at least this is what i see). However, i noticed that by varying the position of the small broad peak, the position of the sharp peak remained more or less unchanged. This is the reason why i said that i think that maybe the width of the peak is the key factor and not so much the degree of overlapping. If we have more than 2 peaks then i think that it becomes more unpredictable to how the positions will change....does that make sense? Thanks

October 14, 2015 at 09:33 am - Permalink

I would say that if you have a tall, narrow peak on top of a low, broad peak, you pretty much have the same situation as what I describe as being able to see individual bumps. In this case, it would be a pimple on a bump :) The main thing that happens in such a case is that the broad peak can look like (and get confused with) any sort of background signal.

Having data points that clearly define the edges of a peak is important to being able to locate it. I have seen cases in which only half the peak is within the data set being fitted- that causes major ambiguity.
Quote:
One of them was very intense and the other one not.....Changing the position of the small peak i could see that the big one was also affected.

This sounds like perhaps (without seeing it myself) the low peak is masquerading as part of the tails of the higher peak.

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com

October 14, 2015 at 04:59 pm - Permalink