The function FILTER2 performs correlation, while the function CONV2 performs convolution. To see what's going on, you need to compare the output of the 'full' option with the output of the 'valid' option. If you compare these two, you'll see that the 'valid' is taking the same submatrix in both cases. The full and valid matrices are actually not dependent on the values of "f".
For example:
a = magic(5)
a =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
f = [1 0; 0 0];
filter2(f,a,'full')
ans =
0 0 0 0 0 0
0 17 24 1 8 15
0 23 5 7 14 16
0 4 6 13 20 22
0 10 12 19 21 3
0 11 18 25 2 9
filter2(f,a,'valid')
ans =
17 24 1 8
23 5 7 14
4 6 13 20
10 12 19 21
The 'valid' result is the (2:5,2:5) submatrix of the 'full' result.
g = [0 0; 0 1];
filter2(g,a,'full')
ans =
17 24 1 8 15 0
23 5 7 14 16 0
4 6 13 20 22 0
10 12 19 21 3 0
11 18 25 2 9 0
0 0 0 0 0 0
filter2(g,a,'valid')
ans =
5 7 14 16
6 13 20 22
12 19 21 3
18 25 2 9
Here also the 'valid' result is the (2:5,2:5) submatrix of the 'full' result.
