When one refers to "the" discrete cosine transform (DCT), it is generally assumed that one means the type II DCT, where the input array $x_k$ ($0 \leq k < N-1$) is even about $k=-1/2$ and $k=N-1/2$.
Is there a similar convention for "the" discrete sine transform? MATLAB defaults to type I, while Mathematica prefers type II. The FFTW docs are silent on the matter.