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I would also mention something about that with both the DFT and the DCT, the signal is conceptually periodic in time. So if I want to find the DFT of the 4-sample sequence 1, 2, 3, 4, it is like finding the DFT of the sequence 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, ..., which has the discontinuity you mention between the 4s and 1s. With the DCT, it's like the periodic sequence is 1, 2, 3, 4, 4, 3, 2, 1, 1, 2,..., which has less discontinuity. (There are different DCT variants on the exact offset of the reflection, but that can be ignored in this discussion.) |