Doing DCT the naive way, the formula is as easy as the DFT. But computing the DCT quickly (like in O(n log n) time) is much harder to understand than the FFT.

Doing DCT the naive way, the formula is as easy as the DFT. But computing the DCT quickly (like in O(n log n) time) is much harder to understand than the FFT. I read a couple of papers and implemented the fast DCT algorithms. The Arai, Agui, Nakajima 8-point DCT uses 13 multiplications. The Lee DCT algorithm is recursive and works on any length that is a power of 2. https://www.nayuki.io/page/fast-discrete-cosine-transform-algorithms https://www.nayuki.io/page/fast-discrete-cosine-transform-al...