On efficient software realization of the prime factor discrete cosine transform

The traditional approach in realizing the prime factor discrete cosine transform (PFDCT) often suffers from two problems. First, although only the Ruritanian mapping is used for input indexing, it requires to perform a series of complicated tests and additions which even outweigh the computational effort of the PFDCT. Second, the additions mentioned above are not carried out in an in-place form. This implies that an auxiliary data array is required to buffer the temporary results generated during the additions. Otherwise, erroneous results will be obtained. In this paper, we propose an efficient indexing scheme for the computation of the PFDCT. By suitably swapping the data, all the additions can be carried out in an inplace form. Furthermore the number of tests required to perform on the indices of the data is greatly reduced. They are achieved by considering the special properties of the Ruritanian mapping.