On the relationship of MDCT transform kernels in Dolby AC-3

The modified discrete cosine transform (MDCT) is widely used in perceptual audio coding algorithm with various types, especially in Dolby AC-3 which has three types for a long transform and two short transforms respectively. A lot of research has been done to pursue fast algorithms of MDCT and efficient ways of implementation as well. In this paper, a developing roadmap of the fast algorithms of MDCT is firstly presented, followed by the analysis to prove that the three types of MDCT can be unified into any one type to simplify the MDCT computation structure in the AC-3 encoder. In the end, the computation complexity of three unifications is compared. The ones using short transform cores have a tiny advantage in the amount of addition. However, this advantage would be darkened due to more circular shifting which the unifications call for.