## Fitting a Gaussian to Data

When fitting a single Gaussian to data, one can take a log and fit a parabola. In matlab, this can be carried out as in the following example:

x = -1:0.1:1; sigma = 0.01; y = exp(-x.*x) + sigma*randn(size(x)); % test data: [p,s] = polyfit(x,log(y),2); % fit parabola to log yh = exp(polyval(p,x)); % data model norm(y-yh) % ans = 1.9230e-16 when sigma=0 plot(abs([y',yh']));In practice, it is good to avoid zeros in the data. For example, one can fit only to the middle third or so of a measured peak, restricting consideration to measured samples that are positive and ``look Gaussian'' to a reasonable extent.

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Gaussians Closed under Convolution