This is probably a silly question, but it's one that's directly relevant to a project of mine and I figured this was the place to go.
I have some objects that contain a 1d and a 2d array of double precision numbers. The 1d array is the 2d array in row major order.
Now, considering the DFT of both these arrays I can quite figure out what the relationship between them would be. I assume the result of the 1d Fourier transform wouldn't be the results of the 2d Fourier transform in row-major order, but I can't quite convince myself of it.
I'm somewhat lacking of a strong intuition on this, any help in conceptualizing this would be greatly appreciated.
Your question is not a silly one. Suppose we take a slice of the 2D Fourier transform of the image. This is equivalent to projecting/accumulating the 2D image onto the line parallel to the line through which we sliced the 2D transform, then taking the 1D Fourier transform of that result. The proof of the projection-slice theorem is not too difficult, once you realize what the correct answer should be.