One way to achieve a fast 1-D DCT computation by sparse matrix factorizations is as follows: Assume N is a power of 2, AN can then be decomposed in the form A N = P N ??? [ A N / 2 0 0 R _ N / 2 ] N ??? N ??? B N ( 2.10 ) where AN/2 is the coefficient matrix for a N/2-point DCT; PN is a permutation matrix which permutes the even rows in increasing order in the top half and the odd rows in decreasi