Condensed recursive structures for discrete cosine transform

In this paper, we propose condensed recursive structures for competing type-two discrete cosine transforms with arbitrary transform length. Based on preaddition and permutation of original input data, the proposed recursive algorithms with fixed computation kernels need fewer recursive loops than the previous methods when the transformed length is not a prime number. In finite length machines, we found that properly selected filter coefficients achieve low round-off errors in their transformations. Furthermore, the proposed structures save computational complexity in the realization of recursive filters, which usually need general multipliers and memory to store total variable filter coefficients.