## GAUSFIT Gaussian Curve Fit

Section: Optimization and Curve Fitting

### 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