# Area under each peak

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camila on 8 Jul 2016
Commented: Star Strider on 21 Feb 2021
Hi, I have a TGA derivative plot with three peaks (two prominant peaks and one shoulder) and I want to get individual gaussian functions to get the area under each peak (which tells how much mass is reduces during heating), could you please tell me how get area under each curve. and also how to get full width half maximum, FWHM and peak center values too.
Thanks

Star Strider on 8 Jul 2016
This was certainly an interesting challenge!
The loop first selects a range of x and y values to make the fit easier, then uses fminsearch to do the fit, calculates the area under the respective Gaussian using trapz and saves it to ‘AUC’, then uses fzero to calculate the full-width-half-maximum value and saves it to ‘FWHM’. The plot simply shows the fitted Gaussians, not ‘AUC’ or ‘FWHM’.
The code:
[d,s,r] = xlsread('chamila De Silva Q16N2.csv');
x = d(:,1);
y = d(:,2);
gausfcn = @(b,x) b(1) .* exp(-((x-b(2)).^2)./b(3)); % Gaussian Function
SSECF = @(b,x,y) sum((y - gausfcn(b,x)).^2); % Sum-Squared-Error Cost Function
[pks,locs] = findpeaks(y, 'MinPeakDist',30, 'MinPeakHeight',0.05); % Find Centres
q = x(locs);
for k1 = 1:size(pks,1)
idxrng = locs(k1)-25 : locs(k1)+25;
[Parms(:,k1), SSE(k1)] = fminsearch(@(b)SSECF(b,x(idxrng),y(idxrng)), [pks(k1); x(locs(k1)); 1]);
AUC(k1) = trapz(x, gausfcn(Parms(:,k1),x));
FWHM(k1) = 2*(x(locs(k1)) - fzero(@(x) gausfcn(Parms(:,k1),x) - pks(k1)/2, x(locs(k1))-5));
end
figure(1)
plot(x, y, 'LineWidth',1.5)
hold on
plot(x(locs), pks, '^r')
for k1 = 1:size(pks,1)
plot(x, gausfcn(Parms(:,k1),x), 'LineWidth',1)
end
hold off
grid
The plot:
Star Strider on 21 Feb 2021
The ‘lims’ constant simply defines the range (±frame length) of ‘idxrng’.