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Efficient Implementations of Cosine-Modulated Pseudo-QMF and MLT (MDCT) Filter Banks in MP3

  • Vladimir Britanak
  • K. R. Rao
Chapter

Abstract

The MPEG-1 and MPEG-2 audio have been the first international audio coding standards specifying the digital format for high quality compression of audio signals. For the time-to-frequency transformation of an audio signal and vice versa, the MPEG-1/2 in layers I and II has adopted a near perfect reconstruction cosine-modulated polyphase quadrature mirror filter (QMF) banks, also referred to as the pseudo-QMF banks. In layer III (known as MP3) it has additionally adopted the perfect reconstruction modulated lapped transform (MLT) which is actually the modified discrete cosine transform (MDCT) associated with the sine windowing function. This chapter describes and compares various efficient implementations of the forward and backward MLT (MDCT) in the MP3 audio coding standard developed in the time period 1990–2012, including the efficient implementation of pseudo-QMF banks for completeness. The efficient MLT (MDCT) implementations are discussed in the context of complete (fast) analysis/synthesis MLT (MDCT) filter banks in the MP3 encoder and decoder. In general, for each efficient forward/backward MLT (MDCT) block transforms implementation are presented: complete formulae or (block) sparse matrix factorizations, the corresponding signal flow graph for short audio block, and the total arithmetic complexity as well as the useful comments related to improving the arithmetic complexity and a possible structural simplification of the algorithm. Finally, the fast analysis and synthesis MLT (MDCT) filter banks for MP3 encoder and decoder are discussed in detail. Appendices provide all the necessary supporting efficient optimized short-length computational modules and tools for completing efficient forward/backward MLT (MDCT) implementations.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Vladimir Britanak
    • 1
  • K. R. Rao
    • 2
  1. 1.Institute of InformaticsSlovak Academy of SciencesBratislavaSlovakia
  2. 2.The University of Texas at ArlingtonArlingtonUSA

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