Find the DFT of the image $x(m, n)$ using the row-column method. Reconstruct the input from the DFT coefficients using the IDFT and verify that they are the same as the input. Verify Parseval's theorem. Express the magnitude of the DFT coefficients in the center-zero format using the $\log$ scale, $\log _{10}(1+|X(k, l)|)$. The origin is at the top-left corner.
*(i)
$$
x(m, n)=\left[\begin{array}{rrrr}
112 & 148 & 72 & 153 \\
120 & 125 & 30 & 99 \\
95 & 120 & 89 & 33 \\
170 & 99 & 109 & 40
\end{array}\right]
$$
(ii)
$$
x(m, n)=\left[\begin{array}{rrrrr}
143 & 107 & 183 & 102 \\
135 & 130 & 225 & 156 \\
160 & 135 & 166 & 222 \\
85 & 156 & 146 & 215
\end{array}\right]
$$
(iii)
$$
x(m, n)=\left[\begin{array}{rrrr}
164 & 127 & 117 & 59 \\
154 & 122 & 104 & 83 \\
129 & 136 & 100 & 60 \\
117 & 128 & 80 & 48
\end{array}\right]
$$