Generalized fast mixed-radix algorithm for the computation of forward and inverse MDCTs

Authors:
Z. G. Gui;Y. Ge;D. Y. Zhang;J. S. Wu
Affiliations:
National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China;Department of Electronic Science and Engineering, Nanjing University, Nanjing 210093, China;Department of Information Science and Engineering, Nanjing University, Nanjing 210093,China;Laboratory of Image Science and Technology, Southeast University, Nanjing 210096, China
Venue:
Signal Processing
Year:
2012

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Abstract

This paper presents a generalized mixed-radix decimation-in-time (DIT) fast algorithm for computing the modified discrete cosine transform (MDCT) of the composite lengths N=2xq^m, m=2, where q is an odd positive integer. The proposed algorithm not only has the merits of parallelism and numerical stability, but also needs less multiplications than that of type-IV discrete cosine transform (DCT-IV) and type-II discrete cosine transform (DCT-II) based MDCT algorithms due to the optimized efficient length-(N/q) modules. The computation of MDCT for composite lengths N=q^mx2^n, m=2, n=2, can then be realized by combining the proposed algorithm with fast radix-2 MDCT algorithm developed for N=2^n. The combined algorithm can be used for the computation of length-12/36 MDCT used in MPEG-1/-2 layer III audio coding as well as the recently established wideband speech and audio coding standards such as G.729.1, where length-640 MDCT is used. The realization of the inverse MDCT (IMDCT) can be obtained by transposing the signal flow graph of the MDCT.