MATLAB: How to fit multiple curves to one curve

curve fitting

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?

Best Answer

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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MATLAB: Area under each peak

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:

MATLAB: How could I calculate and get multiple pulses area under curve value

See if my Answer in Find quasi-periodic peak locations from noisy photon count data will do what you want. (It seems to be a similar problem.) Your data might be easier to fit, so save it as a .mat file and attach (upload) it here if you want specific help with it.

Note that the Savitzky-Golay filter, for all its strengths, may not be the best approach in this instance. Simple lowpass or bandpass filtering may be more appropriate.

Best Answer

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MATLAB: Area under each peak

MATLAB: How could I calculate and get multiple pulses area under curve value

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