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**Fast computational structures for an efficient implementation of the complete TDAC analysis/synthesis MDCT/MDST filter banks.**
*(English)*
Zbl 1178.94038

Summary: A new fast computational structure identical both for the forward and backward modified discrete cosine/sine transform (MDCT/MDST) computation is described. It is the result of a systematic construction of a fast algorithm for an efficient implementation of the complete time domain aliasing cancellation (TDAC) analysis/synthesis MDCT/MDST filter banks. It is shown that the same computational structure can be used both for the encoder and the decoder, thus significantly reducing design time and resources. The corresponding generalized signal flow graph is regular and defines new sparse matrix factorizations of the discrete cosine transform of type IV (DCT-IV) and MDCT/MDST matrices. The identical fast MDCT computational structure provides an efficient implementation of the MDCT in MPEG layer III (MP3) audio coding and the Dolby Labs AC-3 codec. All steps to derive the computational structure are described in detail, and to put them into perspective a comprehensive list of references classified into categories is provided covering new research results achieved in the time period 1999-2008 in theoretical and practical developments of TDAC analysis/synthesis MDCT/MDST filter banks (general mathematical, symmetry and special properties, fast MDCT/MDST algorithms and efficient software/hardware implementations of the MDCT in MP3).

### MSC:

94A11 | Application of orthogonal and other special functions |

65T50 | Numerical methods for discrete and fast Fourier transforms |

94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |

### Keywords:

modified discrete cosine transform; modified discrete sine transform; modulated lapped transform; modulated complex lapped transform; fast computational structure; MPEG audio coding
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\textit{V. Britanak} and \textit{H. J. L. Arriëns}, Signal Process. 89, No. 7, 1379--1394 (2009; Zbl 1178.94038)

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