Algorithms for length 15 and 30 discrete cosine transform

Using sparse matrix factorization, algorithms for length 15 and 30 discrete cosine transforms (DCTs) are developed that require only a single cascaded multiplier in the center of the flow graph. Complete matrix factorizations required to compute the algorithms are presented and it is shown, by computational complexity comparisons, that these algorithms are more efficient than either the radix-2 algorithm or B.G. Lee´s (1987) index mapping algorithm. These algorithms are more efficient than the commonly used radix-2 algorithms for the DCT, especially in terms of the number of required multiplications. They can be used as basic blocks to build algorithms for DCT of length 15*2^k