In the paper “Canonical transformations of the discrete cosine transform” two relations between discrete cosine transforms (DCTs) of types 2 and 4 were presented. One relation is already known, the second was derived by the author of the paper. We would like to point out that the common theory published recently by M. Püschel and J. Moura allows the discovery of existing and new relations between all 16 known types of DCTs and discrete sine transforms (DSTs). In these comments we show that above mentioned relations between DCT-II and DCT-IV can be easily derived from this universal theory. Note also that the second relation was implicitly presented in the fast algorithm of inverse DCT-II derived by B.G. Lee.