91Ó°ÊÓ

Find the 2D-DCT of the following data matrices \(X\), and find the corresponding interpolating function \(P_{2}(s, t)\) for the data points \(\left(i, j, x_{i j}\right), i, j=0,1\) : (a) \(\left[\begin{array}{ll}1 & 0 \\ 0 & 0\end{array}\right]\) (b) \(\left[\begin{array}{ll}1 & 0 \\ 1 & 0\end{array}\right]\) (c) \(\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]\) (d) \(\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\)

Find the 2D-DCT of the data matrix \(X\), and find the corresponding interpolating function \(P_{n}(s, t)\) for the data points \(\left(i, j, x_{i j}\right), i, j=0, \ldots, n-1\). (a) \(\left[\begin{array}{llll}1 & 0 & -1 & 0 \\ 1 & 0 & -1 & 0 \\ 1 & 0 & -1 & 0 \\ 1 & 0 & -1 & 0\end{array}\right]\) (b) \(\left[\begin{array}{llll}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{array}\right]\) (c) \(\left[\begin{array}{llll}0 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0\end{array}\right]\) (d) \(\left[\begin{array}{rrrr}3 & 3 & 3 & 3 \\ 3 & -1 & -1 & 3 \\ 3 & 3 & 3 & 3 \\ 3 & -1 & -1 & 3\end{array}\right]\)