Improved and Extended Mixed-Radix Decimation in Frequency Fast MDCT Algorithm

Recently, a mixed-radix decimation in frequency (DIF) fast MDCT algorithm only for the mixed-radix decompositions or composite lengths N = 3m×2, m > 0, has been proposed in [4]. An improved mixed-radix DIF fast MDCT algorithm both in terms of the regularity and computational complexity is described. Based on observed simple algebraic identities in the original proposed algorithm [4], new formulas are derived resulting in a very regular computational structure. Consequently, the number of arithmetic operations is reduced significantly. Moreover, the improved algorithm is extended to all composite lengths N = 3m×2p, m, p > 0. The improved algorithm defines new sparse matrix factorizations of the MDCT matrix for the composite lengths N = 3 × 2, m, p > 0, and finally it provides new implementations of the forward/backward MDCT in MPEG-1/2 layer III (MP3) audio coding standard.