Apparatus with selective fixed-coefficient filter for performing recursive discrete cosine transforms

An apparatus with new fixed-coefficient recursive structures for computing discrete cosine transforms with the power-of-two length is disclosed. The fixed-coefficient recursive structures are developed from exploration of periodicity embedded in transform bases, whose indices can form a complete residue system or a complete odd residue system. Distinctively,we found that properly selected fixed-coefficient filters achieve lower round-off errors than the nominal variable-coefficient ones for computing DCTs in finite-word-length machines.