Whether it can be done depends more on your model, your data, and your constraints than on the lsqcurvefit function, which is the one most suited to your problem. Choosing the most appropriate initial parameter estimates is also extremely important.
I would use this objective function to fit your data:
% Argument: Matrix ‘tw’ of [t w] (assuming t, w are both COLUMN vectors)
% Parameters: b(1) = a1; b(2) = a2; b(3) = t1; b(4) = t2; b(5) = t3
% Original function:
% f(x) = a1*exp(-t/t1)*cos(w*t)+ a2*exp(-t/t2)+(1-a1-a2)*exp(-t/t3)
f = @(b,tw) b(1).*exp(-tw(:,1)./b(3)).*cos(tw(:,1).*tw(:,2)) + b(2).*exp(-tw(:,1)./b(4)) + (1-b(1)-b(2)).*exp(-tw(:,1)./b(5));
I did my best to be certain it matches your original function. You should proofread it to be sure. Note also that there have to be equal numbers of ‘t’ and ‘w’ data in order to form the ‘[t w]’ matrix.
