The combinations ''c''− − ''d''<sub>''R''</sub> and so on, have precisely the right signs for the combinations to cancel when they are added.
For '''odd''' ''N'' (which are rarely used in practice), ''N''/2 is not an integer, so the MDCT is not simply a shift permutation of a DCT-IV. In this case, the additional shift by half a sample means that the MDCT/IMDCT becomes equivalent to the DCT-III/II, and the analysis is analogous to the above.
