Generating matrices for the discrete sine transforms

In this correspondence, we obtain a general form for the generating matrices of the eight types of discrete sine transforms. These matrix forms can be used to study the performance of the different discrete sine transforms as substitutes of the Karhunen-Loeve transform and will allow us to show in a very straightforward way that the discrete sine transforms, as the discrete cosine transforms, are asymptotically optimal for any finite order Markov process.