I have to implement DCT-II and its inverse which is equivalently given by a forward DCT-III. All from real to real.

I have been checking some paper where it is specified how to do it. However, I already have kissfft as a dependency so I can use FFT and iFFT. I have implemented DCT-II using FFT and an extra space of 4N. I found three different ways to do it here.

For DCT-III, I wounder if I can do the inverse in a clever way (as in the last link) or if I have to implement it using the formula.

  • 1
    $\begingroup$ Look for Chen 1977 famous paper that describes and explicitly shows a fast DCT-II and its inverse for N=8,16, etc... $\endgroup$
    – Fat32
    Commented Nov 24, 2016 at 0:15
  • $\begingroup$ You can find the answer in: dsp.stackexchange.com/questions/2807/… $\endgroup$
    – Nayuki
    Commented Mar 4, 2021 at 5:58


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