ONE-DIMENSIONAL AND 2-DIMENSIONAL ALGORITHMS FOR LENGTH 15 AND 30 DISCRETE COSINE TRANSFORMS

In this brief we show that particular efficiencies in Discrete Cosine Transforms ran be realized if we use sample lengths of 15 and 30. Usin g sparse matrix factorization, 1-D algorithms for length 15 and 30 dis crete cosine transforms (DCT) are first developed and then generalized to the two dimensional DCT. We show that these algorithms are more ef ficient than the commonly used radix-2 algorithms, and general prime f actor algorithms, for the DCT in terms of the number of required multi plications and additions. The new algorithms possess the property of o nly one multiplication in any signal path.