Diagonalizing properties of the discrete cosine transforms

A study of discrete cosine transforms (DCT's) results in the formation of eight types of DCT's for a complete orthonormal eigenvector set. A general form of matrices creates the eigenvectors. Each DCT consists of a class of stationary processes to define suitable asymptotic behavior of the corresponding DCT. With all finite order Markov processes, all of the eight types of DCT's have asymptotical optimality.