First of all: are you sure this is a doublet? The noise on the baseline is almost on the same level as the peak separating notch, so is this doublet reproducible?

Let's assume it is: if you use the multiple peak fit in Origin, at some point you should be given an option that says "Open NLFit" or something similar depending on your version. Then you should get a menu in which you can either set the initial parameters or even fixate them to a certain values. You can also temporarily fix some parameters, optimize the others, then (partially) liberate the fixed parameters and rerun the optimization.

Assuming that you can export and import the data into a readable format, you can use Excel or any number of software packages to manually centroid the peak. There are a number of python scripts for doing centroids as well. The problem is much more complicated if you are searching for peaks and centroiding a number of peaks. For one peak, it is not that difficult.

Junyue Ge: Poor quality data = poor quality results. Start with good quality data using properly developed methods. Why would you use statistical tools or formulas to treat this "peak" as a doublet? It does not appear to be a doublet. As Jürgen notes, the signal is noisy and not the best quality so I think it is incorrect to assume it is a doublet as not enough info is available. Before analyzing the results, why not develop a better LC-MS method to analyze the sample and collect data? Please be sure to have someone with professional training in LC-MS analysis help you at school with this project.

Is the asymmetry present in the main peak (right side) normal? It seems more than two components are present.

You wrote. "since the peak is doublet, there are always two peaks found here". Occasionally surprises occur. If the peak structure was not affected by time-dependent noise or time-independent artifacts, assuming it is a doublet is biased.

How do you know the Fourier transform is the correct (optimum) statistical model for estimating peak components in this signal? Please explain the difference between a based and unbiased method.

After looking at a number of the other comments I went back and looked at the full picture.

If the scales are correct, the peak width at half height is on the order of 8 AMU. As most mass spectrometers have ultimate resolution significantly higher than this value, in the lack of any additional information, there are multiple peaks in this peak. For most quadrupole mass spectrometers, the resolution is at least one amu with a half height width value tending to be generally tuned to about 0.7 amu.

If this is a magnetic sector unit, then the resolution that you are seeing is about 43, which is pretty low.

Even if you fit the peak and find the centroid, there is not much that you will be able to say about the composition of the peak as the resolution is too low.

Hi, Jürgen Weippert John Canham William Letter William C Hutton thank you so much for answering my question!! I am so sorry that I didn't describe my question properly. As you all mentioned, I would also say the peak is in poor quality. Actually I assume it shouldn't be described as 'doublet'. However, I could not find another proper word to describe it. I am sorry for misleading. The data is not acquired by LC-MS, but MALDI MSI instead. The peak is from the spectra of a small Region of Interest in mouse brain section. Due to some reasons, it's tricky to enhance the intensity of the peak and reduce the noise. Thus, I am looking for the method to find centroid value of this peak. Of course, there are a number of peaks like this and would be great if there's a method could do batch process. I will try to double check with parameters in Origin and Python scripts as John Canham mentioned. Thanks again!

Junyue Ge: Thank you for providing a bit more information. Please consider developing a new analysis method, which retains and resolves apart the components present (*Use HPLC), then employ a suitable in-line detection method to obtain more data. This is the more scientific way to understand the results. **Using statistics alone on poor quality data obtained from a poor quality method is not advised. Please be sure to have someone with professional training in HPLC method development and MS analysis help you at school with this project.

How important is your prior information to obtaining a meaningful peak centroid? What do you have to know about the peak to make an optimum estimate for the centroid? Does the centroid estimate have any meaning if there are four peaks with different amplitudes compared to two peaks with similar amplitudes? How do you know this peak is from only one component in the mixture?

You mention the peak" is poor in quality". When the signal-to-noise ratio is low, the datas' information content is low. At some point the information content is insufficient to estimate a meaningful centroid.

As an aside. One can not increase the datas' total signal-to- noise ratio after the measurement is over. Once can filter noise. But all data filtering involves some type of mathematical averaging. Data filtering alone can not decrease the total noise content. However a data noise model that includes objective prior information for the noise can insure the parameter estimates of interest have the minimum uncertainties.