Using the DFT and IDFT, convolve $x(m, n)$ and a $3 \times 3$ Laplacian enhancement filter. Assume periodicity at the borders.
$$
\left[\begin{array}{rrr}
0 & -1 & 0 \\
-1 & 5 & -1 \\
0 & -1 & 0
\end{array}\right]
$$
*(i)
$$
\left[\begin{array}{llll}
7 & 7 & 5 & 1 \\
4 & 4 & 4 & 1 \\
0 & 8 & 4 & 3 \\
5 & 0 & 2 & 1
\end{array}\right]
$$
(ii)
$$
\left[\begin{array}{llll}
1 & 2 & 5 & 1 \\
4 & 1 & 0 & 1 \\
0 & 0 & 3 & 3 \\
5 & 0 & 2 & 4
\end{array}\right]
$$
(iii)
$$
\left[\begin{array}{rrrr}
2 & 3 & 1 & 1 \\
4 & 0 & -4 & 1 \\
0 & 1 & 4 & 3 \\
4 & 0 & -2 & 1
\end{array}\right]
$$