DCT and Inverse DCT Formulas

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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.

By the way, why are you making your own implementation?

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whynot
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whynot

Updated on August 01, 2022

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  • whynot
    whynot over 1 year

    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.

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    • Admin
      Admin about 11 years
      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"?
    • whynot
      whynot about 11 years
      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
    whynot about 11 years
    but what is alpha(u) and alpha (v) in the Inverse DTC formula? That's what I don't get. I'm doing a super simple implementation, just to see how it works. :)
  • Navin
    Navin about 11 years
    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.
  • whynot
    whynot about 11 years
    Yes.. that's what I need to figure out... the values for the DCT are are clearly defined but not for the inverse. Thanks!
  • Navin
    Navin about 11 years
    @whynot If that answered your question, don't forget to accept the answer :)