Mixed-radix algorithm for the computation of forward and inverse MDCTs

  • Authors:

  • Jiasong Wu;Huazhong Shu;Lotfi Senhadji;Limin Luo

  • Affiliations:

  • Lab. of Image Sci. and Techn., Sch. of Comp. Sci. and Eng., Southeast Univ., Nanjing, China. INSERM, Rennes, France. Lab. Traitement du Signal et de l'Image, Univ. de Rennes 1, Centre de Rech. en ...;Lab. of Image Sci. and Techn., Sch. of Comp. Sci. and Eng., Southeast Univ., Nanjing, China and Centre de Recherche en Inf. Biomédicale Sino-Français, Nanjing, China;INSERM, Rennes, France and Lab. Traitement du Signal et de l'Image, Université de Rennes 1, Rennes, France and Centre de Recherche en Inf. Biomédicale Sino-Français, Rennes, France;Lab. of Image Sci. and Techn., Sch. of Comp. Sci. and Eng., Southeast Univ., Nanjing, China and Centre de Recherche en Information Biomédicale Sino-Français, Nanjing, China

  • Venue:
  • IEEE Transactions on Circuits and Systems Part I: Regular Papers
  • Year:
  • 2009

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Abstract

The modified discrete cosine transform (MDCT) and inverse MDCT (IMDCT) are two of the most computationally intensive operations in MPEG audio coding standards. A new mixed-radix algorithm for efficiently 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 algorithm, is obtained by decomposing an N-point MDCT into two MDCTs with the length N/2. The second algorithm, called the radix-3 decimation-in-time algorithm, is obtained by decomposing an N-point MDCT into three MDCTs with the length N/3. Since the proposed MDCT algorithm is also expressed in the form of a simple sparse matrix 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 particularly 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.