$1.(50$p$)$ Assume that you have an image with size of $4$x$4$ pixels. Apply $4$x$42$D$-$DCT transform and $4$x$42$D$-$IDCT transform for that signal, manually. Compare the original signal and reconstructed signal which is obtained from $2$D$-$IDCT. $1.(50$p$)$ Assume that you have an image with size of $4$x$4$ pixels, as given in Q$1.$ Prove that $4$x$42$D$-$DCT transform can be obtained by using $1$D DCT$.$