How to fit multiple curves to one curve?

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Faezeh Manesh 2019-10-1

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https://ww2.mathworks.cn/matlabcentral/answers/483044-how-to-fit-multiple-curves-to-one-curve

评论： Star Strider 2019-10-1

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?

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Answer 1

Star Strider 2019-10-1

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https://ww2.mathworks.cn/matlabcentral/answers/483044-how-to-fit-multiple-curves-to-one-curve#answer_394298

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

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Star Strider 2019-10-1

在 MATLAB Online 中打开

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