Given a $4 \times 4$ image, find the $4 \times 4$ lowpass filtered output using the $3 \times 3$ averaging filter with the borders replicated.
$$
x(m, n)=\left[\begin{array}{llll}
41 & 43 & 45 & 43 \\
40 & 41 & 42 & 41 \\
42 & 38 & 39 & 42 \\
39 & 33 & 37 & 36
\end{array}\right]
$$