Mixed-radix Algorithm for the Computation of Forward and Inverse MDCT

The modified discrete cosine transform (MDCT) and inverse MDCT (IMDCT) are two of the most computational intensive operations in MPEG audio coding standards. A new mixed-radix algorithm for efficient computing the MDCT/IMDCT is presented. The proposed mixed-radix MDCT algorithm is composed of two recursive algorithms. The first algorithm, called the radix-2 decimation in frequency (DIF) algorithm, is obtained by decomposing an -point MDCT into two MDCTs with the length /2. The N N second algorithm, called the radix-3 decimation in time (DIT) algorithm, is obtained by decomposing an -point MDCT into three N MDCTs with the length /3. Since the proposed MDCT algorithm is also expressed in the form of a simple sparse matrix N factorization, the corresponding IMDCT algorithm can be easily derived by simply transposing the matrix factorization. Comparison of the proposed algorithm with some existing ones shows that our proposed algorithm is more suitable for parallel implementation and especially suitable for the layer III of MPEG-1 and MPEG-2 audio encoding and decoding. Moreover, the proposed algorithm can be easily extended to the multidimensional case by using the vector-radix method. Author