How to fit multiple curves to one curve?

Hello Everyone,

Actually, I have a curve which is a result of an experiment ( the black curve in below picture). I need to find some gaussian ( or other function) to fit to this diagram in the following way (The red curves). The idea, is that the main curve has some bumbs and I need to fit some ideal curves to the main curve. Do you have any idea that how I can do it?

Answer 1

[Star Strider]

See: Area under each peak for an example of how to detect the Gaussians (and, if you want to, find thier areas).

[Faezeh Manesh]

Thanks for your answer. Actually, the problem with my data is that the bumps in my curve, are not exactly peaks so I can't use findpeaks function and fit my gaussian curves based on that. Do you have any idea to how to solve this problem? I have attached my data to this message. I really appreciate your assistance

[Faezeh Manesh]

Could you please briefly explain for me that what doas the following part do in Area under each peak code?

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

[Star Strider]

I tried the ischange and findchangepts functions, and I cannot reliably locate what may be the centres of wnat may be the peaks in your data, much less fit them.

This is the best I can do:

[D,S,R] = xlsread('DSCtest.csv');
x = D(:,1);
y = D(:,2);

[cp,sl,in] = ischange(y, 'linear', 'MaxNumChanges',5);
gausfcn = @(b,x) b(1) .* exp(-((x-b(2)).^2)./b(3));                         % Gaussian Function
SSECF = @(b,x,y) norm(y - gausfcn(b,x));                                    % Norm-Error Cost Function
locs = find(cp);
pks = y(cp);

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]);
    Parms(1,k1) = pks(k1);
    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

I leave you to experiment, using different values for 'MaxNumChanges' in the ischange call.

[Faezeh Manesh]

Thank you very much

[Star Strider]

As always, my pleasure!