Sobel filter kernel of large size

Question

I am using a sobel filter of size 3x3 to calculate the image derivative. Looking at some articles on the internet, it seems that kernels for sobel filter for size 5x5 and 7x

Answer 1

Matlab implementation of Daniel's answer:

kernel_width = 9;

halfway = floor(kernel_width/2);
step = -halfway : halfway;

i_matrix = repmat(step,[kernel_width 1]);
j_matrix = i_matrix';

gx = i_matrix ./ ( i_matrix.*i_matrix + j_matrix.*j_matrix );
gx(halfway+1,halfway+1) = 0; % deals with NaN in middle

gy = gx';