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I have a good intuition on how does the 2-D IDCT that underlies the JPEG decoder works, especially after seeing the animation at the bottom of http://en.wikipedia.org/wiki/Discrete_cosine_transform.

I also understand that it can be formulated simply as: idct

However, I'm not sure I understand the intuition behind the forward DCT. It's also expressed as: dct

But for some reason s(x,y,u,v) = r(x,y,u,v). Why is it?

Also, the intuition I have for s is: every T(u,v) is little 8X8 image, where T(0,0) is smooth, and t(8,8) is a checkerboard. The value of a pixel F(3,7) is a linear combination of each of the value of (3,7) in each one of those images. s(3,7,u,v) represents this value in each image.

So for example, I can assume that s(3,7,u,v) is positive for the little images in which (3,7) is closer to white (255), and negative for those in which it is dark (0).

Is this a good intuition? Can you supply a similar, non-math intuition for r?

Thanks!

ihadanny
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    I don't understand the question. – user3344003 Jan 17 '15 at 18:51
  • I dont get the `intuition` did you mean `understanding` instead? DCT converts continuous signal from time to frequency domain in images the time is x or y axis coordinate. IDCT is the reverse conversion. From FFT analogy you can describe `r` and `s` as kernels which are very similar to each other. but to get behind IDCT physical/geometrical kernel basis meaning is not a good idea. If you want just to compute then use FFT for that it is way much faster then FDCT/iFDCT and more documented see here http://stackoverflow.com/a/22779268/2521214 – Spektre Jan 18 '15 at 17:53
  • sorry guys, guess I wasn't clear enough :( I'll try once more in math-overflow, and close this question. – ihadanny Jan 18 '15 at 20:22

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