Understanding the 2D discrete Fourier transform

Question

I just learned about the 1-dimensional discrete Fourier transform which got introduced to me by means of circulant matrices (in the context of convolutions) and noticing that they all have the same eigenvectors. Now I want to learn about the 2D Fourier transform but I couldn't find an explanation so far that satisfied me (most of them solely state the formula without deriving it), which is why I'm asking whether someone knows a good source where the 2D discrete Fourier transform gets properly derived/developed.

Answer 1

I think any image processing course will introduce the 2-D DFT. It is hard to recommend anything in particular not knowing what you want to do with it, but:

• If you are interested in image processing oriented introduction, let me recommend this: https://www.robots.ox.ac.uk/~az/lectures/ia/lect2.pdf

• If you want something a bit broader, I would start with this : https://see.stanford.edu/materials/lsoftaee261/chap8.pdf

• If you want something more theoretical and mathematical, .... then the relevant wikipedia pages are a good place to start in my opinion.

Answer 2

I can recommend "Fouerier Analysis and its applications" by Gerald B. Folland. If you first want to take a look into the book (or can't afford it) you can find a photocopy of it as one of the first google entries when searching the title.