# DCT and Inverse DCT Formulas

I'm implementing DCT, but I don't see the difference with the Inverse DCT formula. Both formula are on the Wikipedia page. The difference looks to be the normalization factor, but I don't see how to implement it.

Encoding

Decoding

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That doesn't sound surprising, although I would expect an additional sign flip somewhere too. What do you mean by "I don't see how to implement it"? –  Hurkyl Oct 26 '12 at 4:52
I'm writing an script that does the actual calculation. I got the DCT working, but don't understand what's different in the Inverse DCT. Specially alpha... –  whynot Oct 26 '12 at 5:11

The fourier transform is a $\pi\over 2$ rotation in the time-frequency plane (see LCT) and the inverse fourier transform $\mathcal F^{-1}\{f(x)\}$ is equivalent to $\mathcal F\{f(-x)\}$ so that kind of symmetry is to be expected. For a really simple implementation, you can just copy-paste those formulas into code.
I believe they are just normalizing factors to ensure that you don't end up with a scaled version of the input after taking the DCT and IDCT. $u$ and $v$ are the indices of the matrix/array. –  Navin Oct 26 '12 at 6:04