One- and two-dimensional algorithms for length 15 and 30 discrete cosine transforms

In this brief we show that particular efficiencies in Discrete Cosine Transforms can be realized if we use sample lengths of 15 and 30. Using sparse matrix factorization, 1-D algorithms for length 15 and 30 discrete cosine transforms (DCT) are first developed and then generalized to the two dimensional DCT. We show that these algorithms are more efficient than the commonly used radix-2 algorithms, and general prime factor algorithms, for the DCT in terms of the number of required multiplications and additions. The new algorithms possess the property of only one multiplication in any signal path.