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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N. Ahmed and K. R. Rao, Orthogonal Transforms for Digital Signal Processing, Springer- Verlag, New York, 1995.
G. Bi, Fast algorithms for type-III DCT of composite sequence lengths, IEEE Trans. Signal Process., vol. 47, no. 7, 2053–2059, 1999.
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.
R. E. Blahut. Fast Algorithms for Digital Signal Processing, Addison-Wesley, Reading, MA., 1984.
S. C. Chan and K. L. Ho, A new two-dimensional fast cosine transform, IEEE Trans. Signal Process., vol. 39, 481–485, 1991.
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.
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.
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.
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.
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.
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.
P. Duhamel and C. Guillemot, Polynomial transform computation of the 2D DCT, Proc. Int. Conf. Acoust, Speech, Signal Process, 1515–1518, 1990.
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.
M. A. Haque, A two dimensional fast cosine transform, IEEE Trans. Acoust, Speech, Signal Process., vol. 33. no. 12, 1532–1539, 1985.
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.
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.
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.
H. J. Nussbaumer and P. Quandalle, Fast polynomial transform computation of the 2-D DCT, Proc. ICDSP, Italy, 276–283, 1981.
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.
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.
A. Tatsaki, C. Dre, T. Storaities and C. Goutis, Prime-factor DCT algorithms, IEEE Trans. Signal process., vol. 43, no. 3, 772–776, 1995.
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.
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.
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.
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.
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.
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).
Y. H. Zeng, Fast algorithms for discrete cosine transform of arbitrary length, Math. Numer. Sinica (in Chinese), vol. 15, no. 3, 295–302, 1993.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media New York
About this chapter
Cite this chapter
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
Download citation
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