Compute the linear convolution of $x(m, n), m, n=0,1,2$, and $h(m, n), m$, $n=0,1$ using the DFT and IDFT and verify your answer by directly computing the convolution. Assume zero-padding at the borders.
*(i)
$$
x(m, n)=\left[\begin{array}{rrr}
1 & 2 & 3 \\
2 & -3 & 1 \\
1 & 2 & 1
\end{array}\right] \text { and } h(m, n)=\left[\begin{array}{rr}
2 & -1 \\
1 & 2
\end{array}\right]
$$
(ii)
$$
x(m, n)=\left[\begin{array}{rrr}
2 & 2 & 3 \\
2 & -3 & -1 \\
1 & -2 & 1
\end{array}\right] \text { and } h(m, n)=\left[\begin{array}{rr}
-2 & -1 \\
1 & 3
\end{array}\right]
$$
(iii)
$$
x(m, n)=\left[\begin{array}{rrr}
1 & -4 & 3 \\
-2 & 3 & 1 \\
1 & -3 & 1
\end{array}\right] \text { and } h(m, n)=\left[\begin{array}{rr}
4 & 1 \\
-1 & 2
\end{array}\right]
$$
(iv)
$$
x(m, n)=\left[\begin{array}{rrr}
2 & 1 & 4 \\
1 & -3 & 2 \\
3 & 2 & 1
\end{array}\right] \text { and } h(m, n)=\left[\begin{array}{rr}
1 & -3 \\
2 & 2
\end{array}\right]
$$
(v)
$$
x(m, n)=\left[\begin{array}{rrr}
1 & 1 & 1 \\
2 & -3 & 4 \\
2 & 2 & 2
\end{array}\right] \text { and } h(m, n)=\left[\begin{array}{rr}
3 & 1 \\
1 & -3
\end{array}\right]
$$