fit gaussian surface over time in matlab

To fit a Gaussian surface over time in MATLAB, you can use the fit function along with the appropriate Gaussian model equation. Here are the steps:

1. Define your time data and the corresponding surface values that you want to fit.
2. Create an anonymous function for the Gaussian model equation. The equation will have parameters that need to be estimated.
3. Use the fit function to fit the Gaussian model to your time and surface data.

Here's an example code snippet that demonstrates the process:

main.m
% Step 1: define time and surface data
time = [1, 2, 3, 4, 5];
surface = [0.2, 0.4, 0.6, 0.8, 1.0];

% Step 2: define Gaussian model equation as an anonymous function
gaussianModel = @(a, b, c, x) a * exp(-((x - b)/c).^2);

% Step 3: fit the Gaussian model to the data
fitResult = fit(time', surface', gaussianModel, 'StartPoint', [1, 3, 1]);

% Step 3 (alternative): fit with custom options
% options = fitoptions(gaussianModel);
% options.StartPoint = [1, 3, 1];
% fitResult = fit(time', surface', gaussianModel, options);

% Display the fit result
disp(fitResult);

% Plot the original data and the fitted curve
plot(time, surface, 'ro'); hold on;
plot(fitResult);
legend('Data', 'Fitted Curve');
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Make sure to customize the Gaussian model equation (gaussianModel) to match your specific needs. The StartPoint argument in the fit function specifies the initial guess for the parameters.

Note that the example assumes you have the Curve Fitting Toolbox installed in MATLAB. If you don't have it, you will need to use alternative methods to fit the Gaussian surface over time.

In addition, make sure to preprocess your data if necessary (e.g., remove noise, take logarithm, etc.) before attempting the fit.