Direct recursive structures for computing radix-r two-dimensional DCT/IDCT/DST/IDST

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 51, Issue 10, 2004, Pages 2017-2030

  Chen, Che Hong ^a   Liu, Bin Da ^a   Yang, Jar Ferr ^a  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CHEBYSHEV APPROXIMATION; COMPUTATIONAL COMPLEXITY; COSINE TRANSFORMS; IIR FILTERS; RECURSIVE FUNCTIONS; VLSI CIRCUITS;

DISCRETE COSINE TRANSFORM (DCT); FAST ALGORITHM; INVERSE DCT (IDCT); MULTIDIMENSIONAL SIGNAL PROCESSING; RECURSIVE STRUCTURE;

DIGITAL SIGNAL PROCESSING;

EID: 7444251761     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2004.835685     Document Type: Article

References (39)

1. K. R. Rao and P. Yip, Discrete Cosine Transform Algorithms, Advantages Applications. New York: Academic, 1990.
2. JPEG Technical Specification, Revision 8, ISO/IEC JTC1/SC2/WG8, CCITT SGV III, JPEG-8-R8, Aug. 1990.
3. Video Codec for Audiovisual Services at p × 64 kbits/s, ITU-T Recommendation H.261, Mar. 1993.
4. Video Coding for Low Bit Rate Communication, ITU-T Recommendation H.263, Mar. 1996.
5. Coding of Moving Pictures and Associated Audio, International Organization for Standardization ISO/IEC JTC1/SC2/WG11, MPEG Video Committee Draft, MPEG 90/176, Rev. 2, Dec. 18, 1990.
6. H. S. Hou, "A fast recursive algorithms for computing the discrete cosine transform," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 1455-1461, Oct. 1987.
7. N. I. Cho and S. U. Lee, "A fast 4 × 4 DCT algorithm for the recursive 2-D DCT," IEEE Trans. Signal Processing, vol. 40, pp. 2166-2173, Sept. 1992.
8. S. C. Chan and K. L. Ho, "A new two-dimensional fast cosine transform algorithm," IEEE Trans. Signal Processing, vol. 39, pp. 481-484, Feb. 1991.
9. S. C. Chan, "Direct methods for computing discrete sinusoidal transforms," Proc. Inst. Elect. Eng. F, vol. 137, pp. 433-442, Dec. 1990.
10. M. A. Haque, "A two-dimensional, fast cosine transforms," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, pp. 1532-1539, June 1985.
11. J. F. Yang and C. P. Fan, "Fast structural two dimensional discrete cosine transform algorithms," IEICE Trans. Fund. Electron. Commun. Comput. Sci., vol. E81-A, pp. 1210-1215, 1998.
12. E. Feig and S. Winograd, "Fast algorithms for the discrete cosine transform," IEEE Trans. Signal Processing, vol. 40, pp. 2174-2193, Sept. 1992.
13. C. Ma, "A fast recursive two dimensional cosine transform," Proc. SPIE Intell. Robots Comput. Vision, vol. 1002, pp. 541-548, 1988.
14. N. I. Cho, I. D. Yun, and S. U. Lee, "On the regular structure for the fast 2-D DCT algorithm," IEEE Trans. Circuit Syst. II, vol. 40, pp. 259-266, Apr. 1993.
15. N.I. Cho and S. U. Lee, "Fast algorithm and implementation of 2-D discrete cosine transform," IEEE Trans. Circuits Syst., vol. 38, pp. 297-305, Mar. 1991.
16. P. Duhamel and C. Guillemot, "Polynomial transform computation of 2-D DCT," in Proc. Int. Conf. Acousics., Speech, Signal Processing, Apr. 1990, pp. 1515-1518.
17. P. Duhamel, "A polynomial-transform based computation of the 2-D DCT with minimum multiplicative complexity," in Proc. Int. Conf. Acousics., Speech, Signal Processing, May 1996, pp. 1515-1518.
18. H. R. Wu and F. J. Paoloui, "A two-dimensional fast cosine transform algorithm based on Hou's approach," IEEE Trans. Signal Processing, vol. 39, pp. 544-546, Feb. 1991.
19. S. S. Kung and M. H. Lee, "An expanded 2-D DCT algorithm based on convolution," IEEE Trans. Consumer Electron., vol. 39, pp. 159-165, Aug. 1993.
20. A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1989.
21. G. Goertzel, "An algorithm for the evaluation of finite trigonometric series," Amer. Math. Month., vol. 65, pp. 34-35, 1958.
22. L. P. Chau and W. C. Siu, "Recursive algorithm for the discrete cosine transform with general length," Electron. Lett., vol. 30, pp. 197-198, 1994.
23. Z. Wang, G. A. Jullien, and W. C. Miller, "Recursive algorithms for the forward and inverse discrete cosine transform with arbitrary length," IEEE Signal Processing Lett., vol. 1, pp. 101-102, July 1994.
24. M. F. Aburdene, J. Zheng, and R. J. Kozick, "Computation of discrete cosine transform using Clenshaw's recurrence formula," IEEE Signal Processing Lett., vol. 2, pp. 155-156, Aug. 1995.
25. Y. H. Chan, L. P. Chau, and W. C. Siu, "Efficient implementation of discrete cosine transform using recursive filter structure," IEEE Trans. Circuits Syst. Video Technol., vol. 4, pp. 550-552, Dec. 1994.
26. J. F. Yang and C. P. Fan, "Compact recursive structures for discrete cosine transform," IEEE Trans. Circuits Syst. II, vol. 47, pp. 314-321, Apr. 2000.
27. J. L. Wang, C. B. Wu, B. D. Liu, and J. F. Yang, "Implementation of the discrete cosine transform and its inverse by recursive structures," in Proc. IEEE Workshop Signal Processing Systems, Oct. 1999, pp. 120-130.
28. C. H. Chen, B. D. Liu, and J. F. Yang, "Recursive architecture for realizing modified discrete cosine transform and its inverse," IEEE Trans. Circuits Syst. II, vol. 50, pp. 38-45, Jan. 2003.
29. H. C. Chiang and J. C. Liu, "Regressive implementations for the forward and inverse MDCT in MPEG audio coding," IEEE Signal Processing Lett., vol. 3, pp. 116-118, Apr. 1996.
30. K. J. R. Liu and C. T. Chiu, "Unified parallel lattice structures for time-recursive discrete cosine/sine/hartley transforms," IEEE Trans. Signal Processing,vol. 41, pp. 1357-1377, Mar. 1993.
31. K. J. R. Liu, J. F. JaJa, and C. T. Chiu, "Theoretical analysis for recursive computation of discrete sinusoidal transforms," in Proc. IEEE Region 10's 9th Annual Int. Conf., 1994, pp. 653-657.
32. K. J. R. Liu, C. T. Chiu, R. K. Kolagotla, and J. F. JaJa, "Optimal unified architectures or the real-time computation of time-recursive discrete sinusoidal transforms," IEEE Trans. Circuits Syst. Video Technol., vol. 4, pp. 168-180, Mar. 1994.
33. E. Frantzeskakis, J. S. Baras, and K. J. R. Liu, "Time-recursive computation and real-time parallel architectures: a framework," IEEE Trans. Signal Processing, vol. 43, pp. 2762-2774, Nov. 1995.
34. V. Srinivasan,and K. J. R. Liu, "VLSI design of high-speed time-recursive 2-D DCT/IDCT processor for video applications," IEEE Trans. Circuits Syst. Video Technol., vol. 6, Feb. 1996.
35. D. Y. Chan, J. F. Yang, and S. Y. Chen, "Regular implementation algorithms of time domain aliasing cancellation," IEE Proc. Vision, Image Signal Processing, vol. 143, pp. 387-392, Dec. 1996.
36. S. S. Demirsoy, R. Beck, I. Kale, and A. G. Dempster, "Novel tecursive-DCT implementations: a comparative study," in Proc. International Workshop Intelligent Data Acquisition Advanced Computing Systems: Technology Applications, July 2001, pp. 120-123.
37. J. F. Yang and C. P. Fan, "Recursive implementation of discrete cosine transforms: with selectable fixed coefficient filters," IEEE Trans. Circuits Syst. II, vol. 46, pp. 211-216, Feb. 1999.
38. C. Y. Hsiung, Elementary Theory of Numbers. Singapore: World Sceientific, 1992.
39. I. Niven, H. S. Zuckerman, and H. L. Montgomery, An Introduction to the Theory of Numbers. New York: Wiley, 1991.