GAUSFIT Gaussian Curve Fit

Usage

The gausfit routine has the following syntax

  [mu,sigma,dc,gain,yhat] = gausfit(t,y,w,mug,sigmag,dcg,gaing).

where the required inputs are

t - the values of the independant variable (e.g., time samples)
y - the values of the dependant variable (e.g., f(t))

The following inputs are all optional, and default values are available for each of them.

w - the weights to use in the fitting (set to ones if omitted)
mug - initial estimate of the mean
sigmag - initial estimate of the sigma (standard deviation)
dcg - initial estimate of the DC value
gaing - initial estimate of the gain

The fit is of the form yhat=gain*exp((t-mu).^2/(2*sigma^2))+dc. The outputs are

mu - the mean of the fit
sigma - the sigma of the fit
dc - the dc term of the fit
gain - the gain of the gaussian fit
yhat - the output samples (the Gaussian fits)

Because the fit is nonlinear, a good initial guess is critical to convergence of the solution. Thus, you can supply initial guesses for each of the parameters using the mug, sigmag, dcg, gaing arguments. Any arguments not supplied are estimated using a simple algorithm. In particular, the DC value is estimated by taking the minimum value from the vector y. The gain is estimated from the range of y. The mean and standard deviation are estimated using the first and second order moments of y. This function uses fitfun.

Example

Suppose we want to fit a cycle of a cosine using a Gaussian shape.

--> t = linspace(-pi,pi); 
--> y = cos(t);
--> [mu,sigma,dc,gain,yhat] = gausfit(t,y);
--> plot(t,y,'rx',t,yhat,'g-');

Which results in the following plot