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Fast MDCT/MDST, MLT, ELT, and MCLT Algorithms

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Cosine-/Sine-Modulated Filter Banks

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Abstract

The perfect reconstruction cosine/sine-modulated analysis/synthesis filter banks such as the MDCT, MLT, MDST, ELT, and MCLT are fundamental processing components for the time-to-frequency transformation of an audio data block in many international audio coding standards, proprietary audio compression algorithms, broadcasting/speech/data communication codecs, as well as open-source royalty free audio/speech codecs for high quality audio/speech compression. Since the computations of cosine/sine-modulated filter banks are the most time-consuming operations in audio coding schemes, the crucial aspect for their applicability is the existence of fast algorithms that allow their efficient software/hardware implementation compared to the direct implementation via their corresponding analytical forms. In this chapter, fast algorithms for the efficient implementation of the forward/backward evenly stacked MDCT/MDST, oddly stacked MDCT/MDST, MLT, ELT, and MCLT block transforms are presented. The emphasis is imposed particularly on basic steps, various tricks (trigonometric and algebraic), and approaches leading to the derivation of final formulae of a fast algorithm. For each fast algorithm complete formulae or a sparse block matrix factorization, a corresponding generalized signal flow graph, the total computational complexity, and a possible structural simplification of the algorithm are presented.

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Change history

  • 08 January 2019

    On p. v, in the third line from top, “in” was inserted after comma to read “. . ., and vice versa, in many sub-band/transform-based schemes . . .”

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Authors and Affiliations

  1. Institute of Informatics, Slovak Academy of Sciences, Bratislava, Slovakia

    Vladimir Britanak

  2. The University of Texas at Arlington, Arlington, TX, USA

    K. R. Rao

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  1. Vladimir Britanak
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  2. K. R. Rao
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Britanak, V., Rao, K.R. (2018). Fast MDCT/MDST, MLT, ELT, and MCLT Algorithms. In: Cosine-/Sine-Modulated Filter Banks. Springer, Cham. https://doi.org/10.1007/978-3-319-61080-1_4

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