How to fit multiple Gaussian peaks to data

Question

How would I fit this data with Gaussian Peaks? I have tried various codes but none have even worked. Note: If I do Log[data], the peaks are more visible

(I have tried the method from here but it got many errors)

@shrx It did not work, I literally copied and pasted the code and made sure my data was correct format. It works for fake data though which was a smaller size — minusatwelfth, Oct 30 '15 at 08:15
Please post your code and an example of your data - what errors did you get? — shrx, Oct 30 '15 at 08:16
http://pastebin.com/0G4Nrfci This is my code which worked (the data is faked), but as soon as I replace 'data' with real data from here http://pastebin.com/aEJAdUuX, it shows many errors. Just copy and paste my code and you will see — minusatwelfth, Oct 30 '15 at 08:19
Your data is very noisy, and I don't see any gaussian peaks other than the large spike near the end of the data. How many peaks do you expect to be there? — shrx, Oct 30 '15 at 08:27
@shrx I don't know how many peaks there are, I'm trying to find that out. Though they are definitely Gaussian — minusatwelfth, Oct 30 '15 at 08:30
@shrx I'm willing to try anything at this point, nothing is working (well that's the only code I found which doesn't have many initial assumptions) — minusatwelfth, Oct 30 '15 at 08:35
@shrx oh right, the data should be Log[data], the peaks are more visible that way — minusatwelfth, Oct 30 '15 at 08:39
@OleksandrR.it's a cyclotron experiment, the detector measures the number of particles every cycle — minusatwelfth, Oct 31 '15 at 05:53

score 6 · Answer 1 · edited Apr 13 '17 at 12:56

Your provided data is very noisy. You can get more information from it if you filter it first. I will apply a LowpassFilter and a logarithmic transform on the $y$ values, and scale down the $x$ values. This usually helps the fitting algorithm.

datat = Transpose[{#[[All, 1]]/1500, 
     Log10[LowpassFilter[#[[All, 2]], .1]]} &@data];
ListPlot[datat, PlotRange -> All, Joined -> True]

Mathematica graphics

Now, you can perform the multi-peak fitting process from the linked discussion.

It's up to you to decide which peaks are signal and which are artifacts. I am providing here the solution with 4 peaks.

With[{n = 4}, 
 resfunc = 
  peakfunc[A[#], μ[#], σ[#], x] & /@ Range[n] /. 
   model[datat, n][[2]]]
(* copied from @Silvia's answer with slight modifications *)
Show@{Plot[Evaluate[resfunc], {x, -5, 10}, 
   PlotStyle -> ({Directive[Dashed, Thick, 
         ColorData["DarkRainbow"][#]]} & /@ 
      Rescale[Range[Length[resfunc]]]), PlotRange -> All, 
   Frame -> True, Axes -> False, ImageSize -> 700], 
  Plot[Evaluate[Total@resfunc], {x, -5, 10}, 
   PlotStyle -> Directive[Thick, Red, Opacity[.5]], PlotRange -> All, 
   Frame -> True, Axes -> False], 
  Graphics[{PointSize[.003], Gray, Line@datat}]}

You will of course have to scale the fitted functions back to the original data, but this should be trivial.

there is supposed to be a lot more peaks. have a look at Logarithm of the data and Joined->True. I think silvia's code cannot handle many peaks — minusatwelfth, Oct 31 '15 at 05:55

How to fit multiple Gaussian peaks to data

1 Answers1