You the have following raster representing (e.g. population).

3	4	3	5	6
2	2	3	1	3
1	5	4	4	4
3	2	3	5	9
1	3	2	3	8

You apply a kernel average 3x3 square filter on it.

Note: kernel filters are also sometimes called focal statistics and in GRASS they are called neighbors function.

Note2: Focal statistics were discussed in class week 2 monday raster analysis.

The output of the filter operation is a new raster with new values for each cell.

aa	ab	ac	ad	ae
ba	bb	bc	bd	be
ca	cb	cc	cd	ce
da	db	dc	dd	de
ea	eb	ec	ed	ee

The new value of bb will be ;

and the new value of ed is: