$($a$)$ The $2$D Discrete Cosine Transform $($DCT$)$ of a $2$D NxN signal $x=x(i,j),i=0,1,2$dotsN$-1$ and $j=0,1,2$dotsN$-1$ can be formed by firstly computing the DCT of all rows of $x$ and storing this in a new matrix $Y$ and then taking the $1$D DCT of all columns of $Y.$ Using the DCT compute the $2$D DCT $(x_{DCT})$ of the following $222$D signal :

$x=\left[\begin{array}{cc}10& 4\\ 3& 10\end{array}\right]$

$($b$)$ As part of a process to compress $x,$ any absolute value of $x_{DCT}$ from part $($a$)$ above that is less than $0\mathrm{.}7$ is assigned to zero to form $x_{DCr-thr.}.$ Using the Inverse DCT formulation compute the Inverse $2$D DCT of $x_{DCT}=$ thr to form $x$ recon

$($c$)$ Compute the mean square error in dBs for the compression process described in part $($c$)$ above.