Advertisement

Perfect Reconstruction Cosine/Sine-Modulated Filter Banks in the Dolby Digital (Plus) AC-3 Audio Coding Standards

  • Vladimir Britanak
  • K. R. Rao
Chapter

Abstract

The Dolby Digital (AC-3) and the Dolby Digital Plus or Enhanced AC-3 (E-AC-3) audio coding standards developed by the Dolby Laboratories are currently the key enabling technologies for high-quality compression of digital audio signals. For the time/frequency transformation of an audio data block, and vice versa, the AC-3 and E-AC-3 have adopted the modified discrete cosine transform (MDCT) as a perfect reconstruction cosine-modulated filter bank. The AC-3 besides the MDCT defines additional two variants of cosine-modulated filter banks called the first and second short transforms. Moreover, the current AC-3 and E-AC-3 codecs for better spectral estimation and for phase angle adjustment have adopted the modified discrete sine transform (MDST) which together with the MDCT forms a complex filter bank. This chapter is devoted to the perfect reconstruction cosine/sine-modulated filter banks used in the Dolby AC-3 and E-AC-3 audio coding standards. The chapter presents: Definitions of the analysis/synthesis AC-3 filter banks, their general symmetry properties both in the time and frequency domains, and their efficient unified implementations. Matrix representations of AC-3 filter banks, [54] their properties and relations among transform (sub-)matrices provide the basis to derive relations between the frequency coefficients and the time domain aliasing data sequences of AC-3 transforms, and in particular, the basis for derivation of a fast algorithm for conversion of frequency coefficients of AC-3 transforms directly in the frequency domain. Finally, conversion methods of the MDCT to MDST frequency coefficients directly in the frequency domain are presented.

Keywords

Dolby Digital AC-3 Dolby Digital Plus or Enhanced AC-3 (E-AC-3) AC-3 filter banks Efficient unified implementations of AC-3 transforms Matrix representations of AC-3 transforms Fast conversion algorithm of frequency coefficients of AC-3 transforms Conversion of the MDCT to MDST frequency coefficients. 

References

  1. 1.
    M. Bosi, S.E. Forshay, High quality audio coding for HDTV: an overview of AC-3, in Proceedings of the 7th International Workshop on HDTV, Torino, Italy, Oct 1994Google Scholar
  2. 2.
    M. Bosi, R.E. Goldberg, Introduction to Digital Audio Coding and Standards (Springer Science+Business Media, New York, 2003), Chap. 5, pp. 103–147, Chap. 14, pp. 371–400CrossRefGoogle Scholar
  3. 3.
    M. Bosi et al., ISO/IEC MPEG-2 advanced audio coding, in 101st AES Convention, Los Angeles, CA, Nov 1996, Preprint #4382Google Scholar
  4. 4.
    G.A. Davidson, M.A. Isnardi, L.D. Fielder, M.S. Goldman, C.C. Todd, ATSC video and audio coding. Proc. IEEE 94(1), 60–76 (2006)CrossRefGoogle Scholar
  5. 5.
    M.F. Davis, The AC-3 multichannel coder, in 95th AES Convention, New York, NY, Oct 1993, Preprint #3774Google Scholar
  6. 6.
    Digital Audio Compression (AC-3) ATSC Standard, Document A/52/10 of advanced television systems committee (ATSC), Audio specialist group T3/S7, Washington D.C., Dec 1995Google Scholar
  7. 7.
    Digital Audio Compression Standard (AC-3, E-AC-3), Revision B, Document A/52B of advanced television systems committee (ATSC), Washington, D.C., Dec 2012Google Scholar
  8. 8.
    L.D. Fielder, D.P. Robinson, AC-2 and AC-3: the technology and its applications, in 5th Australian Regional Convention, Sydney, Australia, April 1995, Preprint #4022Google Scholar
  9. 9.
    L.D. Fielder, M. Bosi, G.A. Davidson, M.F. Davis, C.C. Todd, S. Vernon, AC-2 and AC-3: low-complexity transform-based audio coding, in AES publication collected papers on Digital Audio Bit-Rate Reduction, ed. by N. Gilchrist, C. Grewin (Audio Engineering Society, San Francisco, 1996), pp. 54–72Google Scholar
  10. 10.
    L.D. Fielder et al., Introduction to Dolby digital plus, an enhancement to the Dolby digital coding system, in 117th AES Convention, San Francisco, CA, Oct 2004, Preprint #6196Google Scholar
  11. 11.
    V.K. Madisetti (ed.), The Digital Signal Processing Handbook, vol. 3, 2nd edn., Video, Speech, and Audio Signal Processing and Associated Standards (CRC Press, Boca Raton, 2010), Part I-3: Dolby digital audio coding standards, pp. 3.1–3.46Google Scholar
  12. 12.
    V.K. Madisetti, D.B. Williams (eds.), Digital audio coding: Dolby AC-3, in The Digital Signal Processing Handbook (CRC Press, Boca Raton, 1998), Chap. 41, pp. 41.1–41.21Google Scholar
  13. 13.
    T. Painter, A. Spanias, Perceptual coding of digital audio. Proc. IEEE 88(4), 451–513 (2000)CrossRefGoogle Scholar
  14. 14.
    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. 2161–2164Google Scholar
  15. 15.
    A. Spanias, T. Painter, V. Atti, Audio Signal Processing and Coding (Wiley, Hoboken, 2007), Chap. 6, pp. 145–193, Chap. 10, pp. 263–342Google Scholar
  16. 16.
    C.C. Todd, G.A. Davidson, M.F. Davis, L.D. Fielder, B.D. Link, S. Vernon, AC-3: flexible perceptual coding for audio transmission and storage, in 96th AES Convention, Amsterdam, Feb 1994, Preprint #3796Google Scholar

Efficient Unified Implementations of AC-3 Transforms

  1. 17.
    M. Bosi-Goldberg, Analysis-/synthesis-filtering system with efficient oddly-stacked singleband filter bank using time-domain aliasing cancellation, US Patent Application 5,890,106, Dolby Laboratories, San Francisco, CA, March 1999Google Scholar
  2. 18.
    V. Britanak, The refined efficient implementation of the MDCT in MP3 and comparison with other methods. Technical Report II SAS-2002-02, Sept 2002Google Scholar
  3. 19.
    V. Britanak, New universal rotation-based fast computational structures for an efficient implementation of the DCT-IV/DST-IV and analysis/synthesis MDCT/MDST filter banks. Signal Process. 89(11), 2213–2232 (2009)CrossRefGoogle Scholar
  4. 20.
    V. Britanak, K.R. Rao, The fast generalized discrete Fourier transforms: a unified approach to the discrete sinusoidal transforms computation. Signal Process. 79(12), 135–150 (1999)CrossRefGoogle Scholar
  5. 21.
    V. Britanak, K.R. Rao, A new fast algorithm for the unified forward and inverse MDCT/MDST computation. Signal Process. 82(3), 433–459 (2002)CrossRefGoogle Scholar
  6. 22.
    Y.-C. Chen, C.-W. Tsai, J.-L. Wu, Fast time-frequency transform algorithms and their applications to real-time software implementation of AC-3 codec. IEEE Trans. Consum. Electron. 44(2), 413–423 (1998)CrossRefGoogle Scholar
  7. 23.
    S. Cramer, R. Gluth, Computationally efficient real-valued filter banks based on a modified O 2 DFT, in Proceedings of EUSIPCO’90, Signal Processing V: Theories and Applications (Elsevier Science Publishers B.V., Barcelona, Sept 1990), pp. 585–588Google Scholar
  8. 24.
    R. Gluth, Regular FFT-related transform kernels for DCT/DST–based polyphase filter banks, in Proceedings of the IEEE ICASSP’91, Toronto, Canada, May 1991, pp. 2205–2208Google Scholar
  9. 25.
    C.-M. Liu, W.-C. Lee, A unified fast algorithm for cosine-modulated filter banks in current audio coding standards. J. Audio Eng. Soc. 47(12), 1061–1075 (1999)Google Scholar
  10. 26.
    X. Shao, S.G. Johnson, Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations. Signal Process. 88(6), 1313–1326 (2008)CrossRefGoogle Scholar
  11. 27.
    T. Zhang, S. Liu, J. He, H. Zhang, A new algorithm on short window MDCT for Dolby AC3, in Proceedings of the International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS’2007), Xiamen, China, Nov–Dec 2007, pp. 478–481CrossRefGoogle Scholar
  12. 28.
    T. Zhang, J. He, C. Chen, On the relationship of MDCT transform kernels in AC-3, in Proceedings of the International Conference on Audio, Language and Image Processing, (ICALIP’2009), Shanghai, China, July 2008, pp. 839–842Google Scholar

Matrix Representations of AC-3 Transforms, Relations Between the Frequency Coefficients and the Time Domain Aliasing Data Sequences

  1. 29.
    V. Britanak, On properties, relations, and simplified implementations of filter banks in the Dolby Digital (Plus) AC-3 audio coding standards. IEEE Trans. Audio Speech Lang. Process. 19(5), 1231–1241 (2011)CrossRefGoogle Scholar
  2. 30.
    V. Britanak, H.J. Lincklaen Arriëns, Fast computational structures for an efficient implementation of the complete TDAC analysis/synthesis MDCT/MDST filter banks. Signal Process. 89(7), 1379–1394 (2009)CrossRefGoogle Scholar
  3. 31.
    S.-W. Lee, C.-M. Liu, Transformation from 512–point transform coefficients to 256–point transform coefficients for Dolby AC-3 decoder. Electron. Lett. 35(19), 1614–1615 (1999)CrossRefGoogle Scholar

Fast Algorithm for Conversion of Frequency Coefficients of AC-3 Transforms

  1. 32.
    V. Britanak, Fast conversion algorithm for the Dolby Digital (Plus) AC-3 audio coding standards. IEEE Signal Process Lett. 19(12), 910–913 (2012)MathSciNetCrossRefGoogle Scholar
  2. 33.
    V. Britanak, Fast conversion algorithm for the Dolby Digital (Plus) AC-3 audio coding standards. Presented in the IEEE ICASSP’2013, Vancouver, Canada, May 2013Google Scholar

Conversion Methods of the MDCT to MDST Coefficients Directly in the Frequency domain

  1. 34.
    V. Britanak, New generalized conversion method of the MDCT to MDST coefficients in the frequency domain for arbitrary symmetric windowing function. Digital Signal Process. 23(5), 1783–1797 (2013)MathSciNetCrossRefGoogle Scholar
  2. 35.
    S. Chen, R. Hu, S. Zhang, Estimating spatial cues for audio coding in MDCT domain, in Proceedings of the IEEE International Conference on Multimedia and Expo (IMCE’2009), Cancun, Mexico, June–July 2009, pp. 53–56Google Scholar
  3. 36.
    S. Chen, N. Xiong, J.H. Park, M. Chen, R. Hu, Spatial parameters for audio coding: MDCT domain analysis and synthesis. Multimed. Tools Appl. 48(2), 225–246 (2010)CrossRefGoogle Scholar
  4. 37.
    C.I. Cheng, Method for estimating magnitude and phase in the MDCT domain, in 116th AES Convention, Berlin, Germany, May 2004, Preprint #6091Google Scholar
  5. 38.
    C.I. Cheng, M.J. Smithers, D.N. Lathrop, Improved coding techniques using estimated spectral magnitude and phase derived from MDCT coefficients, US Patent Application US2005/001499, Dolby Laboratories, San Francisco, CA, Aug 2005Google Scholar
  6. 39.
    G.A. Davidson, S.D. Vernon, Method and apparatus for efficient implementation of single-sideband filter banks providing accurate measures of spectral magnitude and phase, US Patent Application #5,727,119, Dolby Laboratories, San Francisco, CA, March 1998Google Scholar
  7. 40.
    B. Edler, S. Geyersberger, Arrangement and method for the generation of a complex spectral representation of a time-discrete signal, International Patent Application WO 2004/013839 A1, Fraunhofer Institute, München, Germany, Feb 2004Google Scholar
  8. 41.
    B. Edler, S. Geyersberger, Device and method for generating a complex spectral representation of a discrete–time signal, US Patent Application No. 11/044786, Fraunhofer Institute, München, Germany, Jan 2005Google Scholar
  9. 42.
    F.J. Harris, On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66(1), 51–83 (1978)CrossRefGoogle Scholar
  10. 43.
    F. Kuech, B. Edler, Aliasing reduction for modified discrete cosine transform domain filtering and its application to speech enhancement, in Proceedings of the IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, New Paltz, NY, Oct 2007, pp. 131–134Google Scholar
  11. 44.
    H. Malvar, A modulated complex lapped transform and its applications to audio processing, in Proceedings of the IEEE ICASSP’99, Phoenix, AR, May 1999, pp. 1421–1424Google Scholar
  12. 45.
    H. Ofir, D. Malah, I. Cohen, Audio packet loss concealment in a combined MDCT-MDST domain. IEEE Signal Process. Lett. 14(12), 1032–1035 (2007)CrossRefGoogle Scholar
  13. 46.
    S.-U. Ryu, K. Rose, A frame loss concealment technique for MPEG AAC, in 120th AES Convention, Paris, France, May 2006, Preprint #6662Google Scholar
  14. 47.
    S.-U. Ryu, K. Rose, An MDCT domain frame-loss concealment technique for MPEG advanced audio coding, in Proceedings of the IEEE ICASSP’2007, vol. I, Honolulu, HI, April 2007, pp. 273–276Google Scholar
  15. 48.
    B.-J. Yoon, H.S. Malvar, Coding overcomplete representations of audio using the MCLT, in Proceedings of the IEEE Data Compression Conference, Snowbird, UT, March 2008, pp. 152–161Google Scholar

Supporting Literature

  1. 49.
    V. Britanak, P. Yip, K.R. Rao, Discrete Cosine and Sine Transforms: General Properties, Fast Algorithms and Integer Approximations (Academic Press/Elsevier Science, Amsterdam, 2007)Google Scholar
  2. 50.
    V. Britanak, A note on the MDCT/MDST and pseudoinverse matrix. Comput. Inform. 23(3), 205–214 (2004)MathSciNetzbMATHGoogle Scholar
  3. 51.
    F.R. Gantmacher, The Theory of Matrices, 2nd edn. (Nauka, Moscow, 1966) (in Russian), English translation: Vol. 1 and 2, Chelsea, New York, 1959Google Scholar
  4. 52.
    G.H. Golub, C.F. Van Loan, Matrix Computations, 3rd edn. (The Johns Hopkins University Press, Baltimore, 1996)zbMATHGoogle Scholar
  5. 53.
    H.S. Malvar, Signal Processing with Lapped Transforms (Artech House, Norwood, 1992)zbMATHGoogle Scholar
  6. 54.
    G.W. Stewart, Matrix Algorithms, Volume I: Basic Decompositions (SIAM Society for Industrial and Applied Mathematics, Philadephia, 1998)CrossRefGoogle Scholar

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

Personalised recommendations