Signal peak integration (signal processing)

I would like to integrate the peaks I have in this plot. I am looking for integrated the peak shown down below. I found a video of how I can do it in the origin software, but I am wondering if this is possible to do the same thing in matlab as well.

A few highlighted point in my plot is that is curve made by the data points are not smooth and also there are some broad peaks. An example file is attached. Thank you!

https://video.search.yahoo.com/video/play;_ylt=AwrFQy0dk01jVnkNy600nIlQ;_ylu=c2VjA3NyBHNsawN2aWQEZ3BvcwMyMw--?p=peak+area+integration+matlab&vid=85371a8ae2016ae6406443e99d571203&turl=https%3A%2F%2Ftse3.mm.bing.net%2Fth%3Fid%3DOVP.mTPp6eDERQsT9ZKpCYvHkgHgFo%26pid%3DApi%26h%3D360%26w%3D480%26c%3D7%26rs%3D1&rurl=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DBtNl5vsl1WI&tit=%3Cb%3EPeak%3C%2Fb%3E+Analysis%3A+Origin+8.6%3A+Regional+%3Cb%3EPeak%3C%2Fb%3E+%3Cb%3EIntegration%3C%2Fb%3E&c=22&sigr=hOZpACMsGq4Q&sigt=Yt_u3iUZek01&sigi=Ux90M_gG59FI&fr=p%3As%2Cv%3Av&h=360&w=480&l=321&age=1321288991&fr=yhs-iba-syn&hsimp=yhs-syn&hspart=iba&type=asbw_8923_CHW_US_tid22076&param1=oBDEqCmKlAYtdwLl9JixRA4UHAG3BKV4TZg7uMGHQWHfAKDe5omiepuIRJDpUxz6&param2=9dUI1n2R0BLDxNuWfiP4aSFOTltNdSPoIx38%2BUf%2FiXrvPdoGmStdlfwLFZYDvqkAJrWWk4yNReCLnBD%2FqPsDZd7olTZcV8HMx1G%2Fk786sE2Tis1g8dJd8zxVWs%2BbKztBnq1TfqUiqPYK9pXifXmJFyorDuCsYXJE71Y6G5tfejDyqA%2FOOYcesmHQFjUmStkEZgOJ3ir4yNI9vw8lwAqcOquqFtE28iC1Y6rlayi2heMuYBKibyndi2xl%2BZvAVIduqG2iBj0J9HGPa83cjHY4LjbDPHlRWec7MxqqyfSvDMkCXjCVwi%2FbmltFGi0Pdb%2FA&param3=NwVEMR%2FzKcG52XsVBYEh2zk2Yklq85vdfspZPoqz2M1qypHRDDTed5vIiOf0QJloIYNIhURx5ygk43IbuWBmnfLApzQNuNyJQuCIFEosygzUObTBvpAdBKtFCFkedGtzXg8BZPONEY8XN9MMyOktF4upJPUjUDsQCabRsqT1bHoQfyzTr8RoM20UF%2BX8gFSQ%2BbtwVgPIiaJMNwoR5vAewaUndCkGrq%2FqoLUjBmVL7708NGMyxtn%2Fl9o%2BOfj%2FVmNF4Qm2YN9Mb8BkPy5nN52gO9jCpXSe6JgFRxPUj4BKDtQt8BrXhKVoQT1dUtpe0tR7CXghpkSUQQtlMGPA5RdeO%2FJpUpfs%2FdK2x7sIRpLNo9GW%2BTqFXdf%2BVbrLjpc07sZlfI6v0NR%2BehEVEK8hHCt5BzlR0PRysM0N3Ci%2F16iYWKKOt1W0%2BOwy9bJT7piW21HY&param4=RV6VDGT7tuWM%2FGPWJLeAv0ykzjGbyHSdEe3QQnVgKZ8%3D&tt=b

Answer 1

[AH]

You may want to try something like below

%% Signal Model
t = linspace(0,1.5,1000);
mu = [1 5 9 13]/10; % position
amp = [3 2 3 1]; % amplitude
sigma = [2 3 6 4]/100; % width
x = 0;
for n = 1:length(mu)
    x = x + amp(n)*exp(-((t - mu(n))/sigma(n)).^2);
end
figure, plot(t,x), xlabel('Time [sec]'), ylabel('Amp.'), grid("on")

%% Find Peaks
[pks,locs,w] = findpeaks(x,t,...
                         'Annotate','extents',...
                         'WidthReference','halfheight');
%% Plot Peak Area
figure
plot(t,x,'LineWidth',2), xlabel('Time [sec]'), ylabel('Amp.'), grid("on")
ylim([min(x)-0.5,max(x)+0.5])
hold("on")
for n = 1:length(pks)
    tstart = locs(n)-w(n);
    tend = locs(n)+w(n);
    ind = sort(find((t >= tstart) & (t <= tend)));
    pax = [t(ind(1)),t(ind(1)),t(ind(end)),t(ind(end))];
    pay = [min(x([ind(1),ind(end)])) pks(n) pks(n) min(x([ind(1),ind(end)]))];
    patch(pax,pay,'yellow','FaceAlpha',0.3)
end

We can play with the factors of the width to cover the desired area manually and approximate the Riemann integral using functions like sum or trapz for each of the highlighted area.

[Shu-An Hsieh]

Thank you. I am thinking if it could be more interactively like if you use mouse click two point and we can get the data in the between. Probably something like ginput or similar things.

[AH]

This is a great idea to have a GUI. At the moment, the best we can do is to do it programatically.

[Shu-An Hsieh]

Is there any GUI function you would recommend to use? Thank you!

[Kevin Holly]

You can make your own with App Designer. Here is a proof of concept for you. Intergrate AH's code in the App attached.