How to perform 2-D DFT via 1-D DFT

Take the 1-D DFT of one image, first row-wise 1-D DFT and followed by column-wise 1-D DFT to create the resulting F1(u,v) .

Answer 1

It actually doesn't matter, but you can do this

 X = randn(8,8);
 Y = fft2(X);
 % ok let's first take the DFT along the rows
 rowdft = fft(X,[],2);
 % now take it along the columns
 coldft = fft(rowdft,[],1);
 max(max(abs(coldft-Y)))

See the maximum difference in absolute value is only on the order of 10^(-15)

Can you perform this same function without using fft2 or fft? that is doing the 2d dft first along the row and then along the col without using fft2 or fft.

Answer 2

Here is an example that shows you how to do it

    X = randn(8,8);
    fft2(X)
    % now use fft
    fft(fft(X).').'

but there is something like "first row-wise 1-D DFT and followed by column-wise 1-D DFT to create the resulting F1(u,v) ". I really dont understand this.