Step1: Perform Row-wise Transform using FFT Flowgraph

For row1 = [0, 1, 2, 1]

For row2 =row4= [1, 2, 3, 2]

For row3 = [2, 3, 4, 3]

Result of row-wise transform is,

$R=\begin{bmatrix}4&-2&0&-2 \\ 8&-2&0&-2 \\ 12&-2&0&-2 \\ 8&-2&0&-2\end{bmatrix}$

Step2: Perform Column-wise Transform using FFT Flowgraph

For column1 = [4, 8, 12, 8]

For column2=column4 = [-2, -2, -2, -2]

For column3 =[0, 0, 0, 0]

Result of column-wise transform,$C=\begin{bmatrix}32&-8&0&-8 \\ -8&0&0&0 \\ 0&0&0&0 \\ -8&0&0&0\end{bmatrix}$

Step3: Scale by $\dfrac1N$

$$DFT[f(x,y)] = \dfrac{1}{N[C]}$$

$DFT[f(x,y)] =\begin{bmatrix}8&-2&0&-2 \\ -2&0&0&0 \\ 0&0&0&0 \\ -2&0&0&0 \end{bmatrix}$