Side note: First draft on Mar 18 2011. Everything popular tends to become a verb. “Let’s Google it.”, “Did you tweet today?”… Well, Gaussian deserves to be a verb also.

**1. 1-D Gaussian Filter**

1-D Gaussian filter can be created according to the normal distribution function below,

The sample matlab code is given below,

A plot of the GUASS will give you the graph below,

**2. 2-D Gaussian Filter**

2-D Gaussian Filter can be created based on the following formula,

The sample matlab code is given below,

The surfc function gives the plot below,

**2. fspeical and imfilter: 2-D Gaussian Filter**

fspecial is used to create several kinds of predefined 2-D filter in matlab, including “gaussian”. imfilter can be used to apply the created filter to multidimensional images.

fspecial takes three input parameters, with the syntax h = fspecial(‘gaussian’, hsize, sigma). hsize can be a vector specifying the number of rows and cols in the generated filter h, or a scalar indicating equal size for height and width. Sigma is the standard deviation marking the thiness of the gaussian.

imfilter takes at least two input parameters, with the syntax B = imfilter(A, H, …), where A is the input matrix, H is the filter. The common options include following,

- Output Size Options:
- ‘same’: output is the same size as input. Default behavior if not specified
- ‘full’: output is full filtered result, which is larger than input.

- Correlation and Convolution Options:
- ‘corr’: use correlation operations for filtering. Default behavior if not specified.
- ‘conv’: use convolution operations for filtering.

This predefined Gaussian filter use the formula below to create the filter,

Sample matlab code is given as below,

The surfc(h) gives the following plot,

**References: **

1. http://www.mathworks.com/help/toolbox/images/ref/fspecial.html

2. http://www.mathworks.com/help/toolbox/images/ref/imfilter.html

please how to plot this gaussian function on matlab

S(t)=Aexp-((t-t0)/2sigma)²