The main reason why this article wasn't intuitive to me is that the toy example is trivial, and the next example (a real image) is very nontrivial. The first e

The main reason why this article wasn't intuitive to me is that the toy example is trivial, and the next example (a real image) is very nontrivial. The first example shows through three lines of runnable Matlab code (sadly, I don't have Matlab and it's not free, but whatever) that if you start with an 8-by-8 matrix of 255 and run the discrete cosine transform, you end up with a sparse matrix with just one nonzero value in the first entry, because "the DCT has compacted the energy of the matrix into the first element referred to as the DC coefficient. The rest of the coefficients are called the AC coefficients." Cool? This doesn't help any more than just telling me that sentence directly. Also, the article doesn't even expand on this fingerhold of familiarity: DC and AC? Like direct current and alternating current, so that first element is in some sense the zero-frequency ("direct current") term, and if the starting example had any variation at all beyond a perfectly uniform field of 255's, you'd start to see "energy" showing up in the "alternating-current" entries? That would start to give some intuition. I guess what I'm saying is this article works, but it works by frustrating the reader just enough that they modify and play with the code (porting it from Matlab if they have to), thereby gaining the intuitive understanding that the article promises.