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Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

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Abstract

This chapter presents fast algorithms that have recently been developed for the computation of the type-I, -II and -III multidimensional (MD) discrete cosine transforms (DCTs). Some of the concepts used in Chapter 6 are extended for the computation of MD DCTs.

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References

  1. N. Ahmed and K. R. Rao, Orthogonal Transforms for Digital Signal Processing, Springer- Verlag, New York, 1995.

    Google Scholar 

  2. G. Bi, Fast algorithms for type-III DCT of composite sequence lengths, IEEE Trans. Signal Process., vol. 47, no. 7, 2053–2059, 1999.

    Article  MathSciNet  Google Scholar 

  3. G. Bi, Y. H. Zeng and Y. Chen, Prime factor algorithm for multi-dimensional discrete cosine transform, IEEE Trans. Signal Process., vol. 49, no. 9, 2156–2161, 2001.

    Article  MathSciNet  Google Scholar 

  4. R. E. Blahut. Fast Algorithms for Digital Signal Processing, Addison-Wesley, Reading, MA., 1984.

    Google Scholar 

  5. S. C. Chan and K. L. Ho, A new two-dimensional fast cosine transform, IEEE Trans. Signal Process., vol. 39, 481–485, 1991.

    Article  MATH  Google Scholar 

  6. S. C. Chan and K. L. Ho, Efficient index mapping for computing discrete cosine trans-form, Electron. Lett., vol. 25, no. 22, 1499–1500, 1989.

    Article  MATH  Google Scholar 

  7. S. C. Chan and K. L. Ho, Fast algorithm for computing the discrete cosine transform, IEEE Trans. Circuits Syst. II, vol. 39, no. 3, 185–190, 1992.

    Article  MATH  Google Scholar 

  8. N. I. Cho and S. U. Lee, A fast 4x4 algorithm and implementation of 2-D discrete cosine transform, IEEE Trans. Signal Process., vol. 40, no. 9, 2166–2173, 1992.

    Article  MATH  Google Scholar 

  9. N. I. Cho and S. U. Lee, Fast algorithm and implementation for 2-D discrete cosine transform, IEEE Trans. Circuits Syst. II, vol. 38, no. 3, 297–305, 1991.

    Google Scholar 

  10. N. I. Cho and S. U. Lee, On the regular structure for the fast 2D DCT algorithm, IEEE Trans. Circuits Syst. II, vol. 40, no. 4, 259–266, 1993.

    Article  MATH  Google Scholar 

  11. N. I. Cho and S. U. Lee, DCT algorithms for VLSI parallel implementations, IEEE Trans. Acoustics, Speech, Signal Process., vol. 38, no. 1, 121–127, 1990.

    Article  Google Scholar 

  12. P. Duhamel and C. Guillemot, Polynomial transform computation of the 2D DCT, Proc. Int. Conf. Acoust, Speech, Signal Process, 1515–1518, 1990.

    Google Scholar 

  13. W. H. Fang, N. C. Hu and S. K. Shih, Recursive fast computation of the two-dimensional discrete cosine transform, IEE Proc. Vision, Image and Signal Processing, vol. 146, no. 1, 25–33, 1999.

    Article  Google Scholar 

  14. M. A. Haque, A two dimensional fast cosine transform, IEEE Trans. Acoust, Speech, Signal Process., vol. 33. no. 12, 1532–1539, 1985.

    Article  MATH  Google Scholar 

  15. D. C. Kar and V. V. B. Tao, On the prime factor decomposition algorithm for the discrete sine transform, IEEE Trans. Signal Process., vol. 42, no. 11, 3258–3260, 1994.

    Article  Google Scholar 

  16. B. G. Lee, Input and output index mapping for a prime-factor-decomposed computation of discrete cosine transform, IEEE Trans. Acoust., Speech, Signal Process., vol. 37, no. 2, 237–244, 1989.

    Article  MATH  Google Scholar 

  17. P. Lee and F. Y. Huang, An efficient prime-factor algorithm for the discrete cosine trans-form and its hardware implementations, IEEE Trans. Acoust, Speech, Signal Process., vol. 42, no. 8, 1996–2005, 1994.

    Google Scholar 

  18. H. J. Nussbaumer and P. Quandalle, Fast polynomial transform computation of the 2-D DCT, Proc. ICDSP, Italy, 276–283, 1981.

    Google Scholar 

  19. J. Prado and P. Duhamel, A polynomial transform based computation of the 2-D DCT with minimum multiplicative complexity, Proc. ICASSP, vol. 3, 1347–1350, 1996.

    Google Scholar 

  20. Y. L. Siu and W. C. Siu, Variable temporal-length 3-D discrete cosine transform coding, IEEE Trans. Image Processing, vol. 6, no. 5, 758–763, 1997.

    Article  Google Scholar 

  21. A. Tatsaki, C. Dre, T. Storaities and C. Goutis, Prime-factor DCT algorithms, IEEE Trans. Signal process., vol. 43, no. 3, 772–776, 1995.

    Article  Google Scholar 

  22. Z. S. Wang, Z. Y. He, C.R. Zou and J. D. Z. Chen, A generalized fast algorithm for n-D discrete cosine transform and its application to motion picture coding, IEEE Trans. Circuits Syst. II, vol. 46, no. 5, 617–627, 1999.

    Article  MATH  Google Scholar 

  23. Y. H. Zeng, G. Bi and A. R. Leyman, New polynomial transform algorithm for multidi-mensional DCT, IEEE Trans. Signal Process., vol. 48, no. 10, 2814–2821, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  24. Y. H. Zeng, G. Bi and A. C. Kot, New algorithm for multidimensional type-III DCT, IEEE Trans. Circuits Syst. II, vol. 47, no. 12, 1523–1529, 2000.

    Article  MATH  Google Scholar 

  25. Y. H. Zeng, G. Bi and A. R. Leyman, New algorithm for r-dimensional DCT-II, IEE Proc., Vision, Image and Signal Processing, vol. 148, no. 1, 1–8, 2000.

    Article  Google Scholar 

  26. Y. H. Zeng, G. Bi and Z. P. Lin, Combined polynomial transform and radix-q algorithm for multi-dimensional DCT-III, Multidimensional System Signal Process., vol. 13, no. 1, 79–99, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  27. Y. H. Zeng, L. Z. Cheng and M. Zhou, Parallel Algorithms for Digital Signal Process-ing, National University of Defense Technology Press, Changsha, P. R. China, 1998 (in Chinese).

    Google Scholar 

  28. Y. H. Zeng, Fast algorithms for discrete cosine transform of arbitrary length, Math. Numer. Sinica (in Chinese), vol. 15, no. 3, 295–302, 1993.

    MathSciNet  MATH  Google Scholar 

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Bi, G., Zeng, Y. (2004). Fast Algorithms for MD Discrete Cosine Transform. In: Transforms and Fast Algorithms for Signal Analysis and Representations. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8220-0_7

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  • DOI: https://doi.org/10.1007/978-0-8176-8220-0_7

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6499-6

  • Online ISBN: 978-0-8176-8220-0

  • eBook Packages: Springer Book Archive

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