Compute the two-dimensional DFT [4x4] for the following 4x4 image $ \begin{matrix} 0.5 & 0.5 & 0.5 & 0.5 \\ 0.5 & 0.5 & 0.5 & 0.5\\ 0.5 & 0.5 & 0.5 & 0.5\\ 0.5 & 0.5 & 0.5 & 0.5 \end{matrix} $
I know that DFT is separable by dimensions – one can calculate 4 vertical transforms first, then 4 horizontal ones
For each row we get [2 0 0 0] in the first and third row and zero elsewhere.
For each column we get [1 0 1 0] in the first and third column and zero elsewhere.
How from this two one-dimensional dfts obtain two-dimensional one?