## Examples of linear convolutional filters

The sharpening filter perhaps needs a bit explanation. Suppose the pixel under the center of the filter has value $v = x+d$, while all the pixels around have value $v_a = x$, then after filtering:

Obviously, when the difference between the pixel and its environment is zero, the filter will not have any effect, but when there is a difference, it’s amplified by a factor of $17/9$. Therefore this is called a sharpening filter.