fouriertransformation on a picture using 1D DFT

Hello, I'm new to this forum and unfortunately already have a question.

I have to transform a picture using a NxN DFT matrix I already constructed using matlab (for N=16 and a 1D signal f=cos((6πn/16)). Can I use the same N or do I need to adjust it to the picture? And then I have to transfer the picture to the frequency domain by applying first the column iteration and then the row iteration of the DFT, in order to save calculation time. Can someone please give me a hint on how to create the loop for this (for....end)?

Hopefully someone can help me with this Thank you already mark

Answer 1

[Wayne King]

Unless I'm missing something, if you have the DFT matrix, then multiply the image matrix by that DFT matrix, then take the transpose (without conjugating the entries!) and then multiply that result by the DFT matrix and tranpose that result (not conjugating)

So using fft() this is

   x = randn(4,4);
   xdft = fft(x); % equivalent to multiplying x by the DFT matrix.
   ydft = fft(xdft.'); 
   % equivalent to multiplying the xdft.' by DFT matrix
   % finally
   ydft = ydft.';

Compare the above to

    fft2(x)

Answer 2

[zurbruegg mark]

First thank you for answering so quickly!

In principle that's correct. However I have to work with the NxN DFT matrix I already designed. The was it is supposed to work is, I multiply the x' row of my image matrix with the DFT and get a vector v. This I will then have to iterate over all columns and its transpose over all rows using loops. With that I should get my picture faster in the frequency domain than by using a 2D DFT. Do I have to choose N the same size as my picture matrix? And how would I include the loops? I will need a 2D DFT in the end, since I need to visualize the result with a logarithmic scale.

Sorry If I was unclear before (or still am)...