Relation between the Karhunen-Loeve and sine transforms

In an earlier paper it was demonstrated that the cosine transform can be derived from the optimum (Karhunen-Loÿve) transform of a first-order Markov source in the limiting case when the adjacent data element correlation coefficient tends to unity. The purpose of the letter is to show that, in the alternative limiting case when the correlation tends to zero, the sine transform results.