fit two exponential decays with exponential function with shared time constant. in matlab

main.m
% Generate data with two decaying exponential functions
t = 0:0.1:10; % Time vector
y1 = 5 * exp(-0.5 * t); % First decay
y2 = 3 * exp(-0.5 * t); % Second decay

% Combine the two decay functions
y = y1 + y2;

% Fit the data to the model
model = @(c, t) c(1) * exp(-0.5 * t) + c(2) * exp(-0.5 * t);
c0 = [1, 1]; % Initial guess for the coefficients
coefficients = lsqcurvefit(model, c0, t, y);

% Plot the results
fit1 = coefficients(1) * exp(-0.5 * t);
fit2 = coefficients(2) * exp(-0.5 * t);
fit = fit1 + fit2;

plot(t, y, 'ko', t, fit, 'r-');
legend('Data', 'Fitted curve');
xlabel('Time');
ylabel('Amplitude');
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