fit exp(-t2/tau+i(wt2-phi) to exponential with oscillation in matlab

To fit the function exp(-t^2/tau + i*(w*t - phi)) to an exponential with oscillation in MATLAB, you can use the curve fitting toolbox in MATLAB. Here is an example of how to do it:


main.m
% Generate some example data
t = linspace(0, 10, 100);
y = real(exp(-t.^2/tau + 1i*(w*t - phi))) + randn(size(t))*0.05;

% Define the function to fit
fun = @(x, t) real(exp(-t.^2/x(1) + 1i*(x(2)*t - x(3))));

% Initial guess for parameters
x0 = [tau; w; phi];

% Perform the curve fitting
x = lsqcurvefit(fun, x0, t, y);

% Extract the fitted parameters
tau_fit = x(1);
w_fit = x(2);
phi_fit = x(3);

% Plot the fitted function
figure
plot(t, y, 'o', t, real(exp(-t.^2/tau_fit + 1i*(w_fit*t - phi_fit))), '-')
legend('Data', 'Fitted Function')
xlabel('t')
ylabel('y')
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In this code, t represents the independent variable, y represents the dependent variable, and tau, w, and phi are the parameters you want to fit. The lsqcurvefit function is used to perform the least square curve fitting. The fun function represents the function you want to fit, and x0 is the initial guess for the parameters.

After fitting, the code plots both the original data and the fitted function for comparison. The fitted parameters tau_fit, w_fit, and phi_fit can be used for further analysis.

Please note that the actual implementation might vary depending on the specific problem and the behavior of your data.