A survey of efficient MDCT implementations in MP3 audio coding standard: Retrospective and state-of-the-art.

*(English)*Zbl 1217.94028Summary: This tutorial paper describes various efficient implementations (published and new unpublished) of the forward and backward modified discrete cosine transform (MDCT) in the MPEG layer III (MP3) audio coding standard developed in the time period 1990–2010, including the efficient implementation of polyphase filter banks for completeness. The efficient MDCT implementations are discussed in the context of (fast) complete analysis/synthesis MDCT filter banks in the MP3 encoder and decoder. In general, for each efficient forward/backward MDCT block transforms implementation are presented: complete formulas or sparse matrix factorizations of the algorithm, the corresponding signal flow graph for the 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, all efficient forward/backward MDCT implementations are compared both in terms of the arithmetic complexity and structural simplicity. It is important to note that almost all presented algorithms can be also used for the \(2^{n}\)-length data blocks in others MPEG audio coding standards and proprietary audio compression algorithms.

##### MSC:

94A11 | Application of orthogonal and other special functions |

94A29 | Source coding |

94A14 | Modulation and demodulation in information and communication theory |

##### Keywords:

modified discrete cosine transform; modulated lapped transform; polyphase filter bank; MPEG layer III audio coding##### Software:

MDCT/MDST
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\textit{V. Britanak}, Signal Process. 91, No. 4, 624--672 (2011; Zbl 1217.94028)

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##### References:

[1] | Information Technology–Coding of Moving Pictures and Associated Audio for Digital Storage Media at up to about 1.5Mbit/s, Part 3: Audio, ISO/IEC JTC1/SC29/WG11 MPEG, International Standard 11172-3 (MPEG-1), 1992. |

[2] | Information Technology–Generic Coding of Moving Pictures and Associated Audio, Part 3: Audio, ISO/IEC JTC1/SC29/WG11 MPEG, International Standard 13818-3 (MPEG-2), 1994. |

[3] | Bosi, M.; Goldberg, R. E.: Introduction to digital audio coding and standards, (2003) |

[4] | J.P. Princen, A.W. Johnson, A.B. Bradley, Sub-band/transform coding using filter bank designs based on time domain aliasing cancellation, in: Proceedings of the IEEE ICASSP’87, Dallas, TX, April 1987, pp. 2161–2164. |

[5] | Princen, J. P.; Bradley, A. B.: Analysis/synthesis filter bank based on time domain aliasing cancellation, IEEE transactions on acoustics, speech, and signal processing 34, No. 5, 1153-1161 (1986) |

[6] | H.S. Malvar, A modulated complex lapped transform and its application to audio processing, in: Proceedings of the IEEE ICASSP’99, Phoenix, AR, May 1999, pp. 1421–1424. |

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