# How to Extract/Fit bell curves under a time series...

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Claudio Iturra on 12 Apr 2023
Commented: Star Strider on 13 Apr 2023
Hello everyone, I'm trying to fit curves under a time series in order to extract the area and compare it. I tried the fit code, but it only takes the maximum and minimum amplitudes, not the entire peak or curve. Is there any way to calculate the area of multiple curves that are in the time series? I will apreciate any help///
Mathieu NOE on 12 Apr 2023
It would help if you share your code and data
Claudio Iturra on 13 Apr 2023
Hello Mathiei, sorry for not attach the code...
clear all,close all;
x = linspace(0,1,1000);
Pos = [1 2 3 5 7 8]/10;
Hgt = [3 4 4 2 2 3];
Wdt = [2 6 3 3 4 6]/100;
for n = 1:length(Pos)
Gauss(n,:) = Hgt(n)*exp(-((x - Pos(n))/Wdt(n)).^2);
end
% my raw time serie consists of a sum of bell curves + some noise....
PeakSig = sum(Gauss);
subplot(1,2,1)
plot(x,PeakSig,'r')
subplot(1,2,2)
plot(x,Gauss,'--',x,PeakSig)
%--------------------
% Now I am looking for the method to reconstruct the
% bell curves (inverse) from the time series in order to evaluate
% the area under each bell curves.

Star Strider on 13 Apr 2023
Edited: Star Strider on 13 Apr 2023
In order to uniquely identify the peaks and identify their parameters, it is necessary to restrict the range of ‘x’ values for each peak. That is done by identifying the valleys (‘vys’) between them and using those index values to restrict the regression —
% clear all,close all;
x = linspace(0,1,1000);
Pos = [1 2 3 5 7 8]/10;
Hgt = [3 4 4 2 2 3];
Wdt = [2 6 3 3 4 6]/100;
for n = 1:length(Pos)
Gauss(n,:) = Hgt(n)*exp(-((x - Pos(n))/Wdt(n)).^2);
end
% my raw time serie consists of a sum of bell curves + some noise....
PeakSig = sum(Gauss);
subplot(1,2,1)
plot(x,PeakSig,'r')
subplot(1,2,2)
plot(x,Gauss,'--',x,PeakSig)
%--------------------
% Now I am looking for the method to reconstruct the
% bell curves (inverse) from the time series in order to evaluate
% the area under each bell curves.
[pks,plocs] = findpeaks(PeakSig);
[vys,vlocs] = findpeaks(-PeakSig);
vlocsv = [1 vlocs numel(x)];
objfcn = @(b,x) b(1).*exp(-(x-b(2)).^2/b(3));
for k = 1:numel(plocs)
idxrng = vlocsv(k) : vlocsv(k+1);
B0 = [pks(k); x(plocs(k)); 1E-6];
B(:,k) = fminsearch(@(b) norm(PeakSig(idxrng)-objfcn(b,x(idxrng))), B0);
end
Parameters = array2table(B, 'VariableNames',compose('Peak #%d',1:numel(plocs)), 'RowNames',{'Hgt','Pos','Wdt'})
Parameters = 3×6 table
Peak #1 Peak #2 Peak #3 Peak #4 Peak #5 Peak #6 __________ _________ _________ __________ ________ _________ Hgt 3.1865 3.9598 4.1999 2 2.2686 2.9937 Pos 0.10288 0.20114 0.29498 0.5 0.71014 0.79574 Wdt 0.00056422 0.0040159 0.0012794 0.00090003 0.002346 0.0042675
% figure % Plot Individual Peaks
% tiledlayout(3,2)
% for k = 1:size(B,2)
% nexttile
% Bk = B(:,k)
% plot(x, objfcn(B(:,k),x))
% hold on
% xline(B(2,k), '-', string(B(2,k)))
% hold off
% end
figure
plot(x, PeakSig, '-r')
hold on
for k = 1:size(B,2)
Gfit(k,:) = objfcn(B(:,k),x);
plot(x, Gfit(k,:), '--')
AUC(k) = trapz(x, Gfit(k,:));
end
hold off
text(Parameters{2,:}, Parameters{1,:}, "Area = "+AUC, 'Horiz','left', 'Vert','bottom')
EDIT — (13 Apr 2023 at 14:00)
Forgot about the areas. Now included.
.
Claudio Iturra on 13 Apr 2023
Wow, Thaks again Strider...currently reading the --help MinPeakProminence, looks great. Usually I just filter the data to avoid noise problems related to findpeacks. Will try MinPeakProminence....
Star Strider on 13 Apr 2023
As always, my pleasure!
Filtering isn’t always the complete solution, because there may be peaks that would be passed by the filter yet not be the desired peaks for a specific analysis. That’s when 'MinPeakProminence' really helps!

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