An Efficient Prime-Factor Algorithm for the Discrete Cosine Transform and Its Hardware Implementations

IEEE Transactions on Signal Processing

Volumn 42, Issue 8, 1994, Pages 1996-2005

  Lee, PeiZong ^a   Huang, Fang Yu ^b  

^a INSTITUTE OF INFORMATION SCIENCE   (Taiwan)

^b National Bureau of Standard ^*  (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; MATHEMATICAL TRANSFORMATIONS; OPTIMIZATION; RANDOM PROCESSES; SIGNAL THEORY; VLSI CIRCUITS;

DISCRETE COSINE TRANSFORM; INPUT INDEX MAPPING; KARHUNEN LOEVE TRANSFORMATIONS; PRIME FACTOR ALGORITHM;

DIGITAL SIGNAL PROCESSING;

EID: 0028484419     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.301838     Document Type: Article

References (35)

1. C. S. Burrus, “Index mappings for multidimensional formulation of the DFT and convolution,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-25, no. 3, pp. 239–242, June 1977.
2. C. S. Burrus, “Bit reverse unscrambling for a radix-2 M FFT,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, 1987, pp. 1809–1810.
3. C. S. Burrus, “Unscrambling for fast DFT algorithms,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 36, no. 7, pp. 1086–1087, July 1988.
4. C. S. Burrus and P. W. Eschenbacher, “An in-place, in-order prime factor FFT algorithm,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-29, no. 4, pp. 806–817, Aug. 1981.
5. C. Chakrabarti and J. JáJ á, “Systolic architectures for the computation of the discrete Hartley and the discrete cosine transforms based on prime factor decomposition,” IEEE Trans. Comput., vol. 39, no. 11, pp. 1359–1368, Nov. 1990.
6. S. C. Chan and K. L. Ho, “Prime factor real-valued Fourier, cosine, and Hartley transforms,” Sixth European Signal Processing Conf. (Brussels, Belgium), Aug. 1992, pp. 1045–1048.
7. N. I. Cho and S. U. Lee, “DCT algorithms for VLSI parallel implementations,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, no. 1, pp. 121–127, Jan. 1990.
8. M. T. Heideman, “Computation of an odd-length DCT from a real-valued DFT of the same length,” IEEE Trans. Signal Processing, vol. 40, no. 1, pp. 54–61, Jan. 1992.
9. H. S. Hou, “A fast recursive algorithm for computing the discrete cosine transform,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, no. 10, pp. 1455–1461, Oct. 1987.
10. D. P. Kolba and T. W. Parks, “A prime factor FFT algorithm using high-speed convolution,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-25, no. 4, pp. 281–294, Aug. 1977.
11. H. T. Kung and C. E. Leiserson, Introduction to VLSI Systems. Reading, MA: Addison-Wesley, 1980.
12. B. G. Lee, “A new algorithm to compute the discrete cosine transform,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, no. 6, pp. 1243–1245, Dec. 1984.
13. B. G. Lee, “Input and ouput index mappings for a prime-factor decomposed computation of discrete cosine transform,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, no. 2, pp. 237–244, Feb. 1989.
14. P.-Z. Lee and F. Y. Huang, “Restructured recursive DCT and DST algorithms,” IEEE Trans. Signal Processing, to be published.
15. P.Z. Lee and Z. M. Kedem, “Mapping nested loop algorithms into multidimensional systolic arrays,” IEEE Trans. Parallel Dist. Syst., vol. 1, pp. 64–76, Jan. 1990.
16. W. Li, “A new algorithm to compute the DCT and its inverse,” IEEE Trans. Signal Processing, vol. 39, no. 6, pp. 1305–1313, June 1991.
17. D. P. K. Lun, R. Chan, and W. C. Siu, “Yet a fast address generation scheme for the computation of prime factor algorithms,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, 1990, pp. 1499–1502.
18. D. P. K. Lun and W. C. Siu, “On prime factor mapping for the discrete Hartley transform,” IEEE Trans. Signal Processing, vol. 40, no. 6, June 1992.
19. M. J. Narasimha and A. M. Peterson, “On the computation of the discrete cosine transform,” IEEE Trans. Commun., vol. COM-26, pp. 934–936, June 1978.
20. H. J. Nussbaumer, “Fast Fourier Transform and Convolution Algorithms,” in Springer Series in Information Sciences. New York: Springer-Verlag, 1981.
21. K. R. Rao and P. Yip, Discrete Cosine Transform: Algorithms, Advantages, and Applications. New York: Academic, 1990.
22. J. H. Rothweiler, “Implementation of the in-order prime factor transform for variable sizes,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-30, no. 1, pp. 105–107, Feb. 1982.
23. H. V. Sorensen, D. L. Jones, C. S. Burrus, and M. T. Heideman, “On computing the discrete Hartley transform,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 33, no. 4, pp. 1231–1238, Oct. 1985.
24. H. V. Sorensen, D. L. Jones, M. T. Heideman, and C. S. Burrus, “Real- valued fast Fourier transform algorithms,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, no. 6, pp. 849–863, June 1987.
25. C. Temperton, “A note on prime factor FFT algorithms,” J. Computational Physics, vol. 52, pp. 198–204, 1983.
26. C. Temperton, “Implementation of a self-sorting in-place prime factor FFT algorithm,” J. Computational Physics, vol. 58, pp. 283–299, 1985.
27. C. Temperton, “Implementation of a prime factor FFT algorithm on CRAY-1,” Parallel Computing, vol. 6 pp. 99–108, 1988.
28. M. Vetterli and H. J. Nussbaumer, “Simple FFT and DCT algorithm with reduced number of operations,” Signal Processing, vol. 6, no. 4, pp. 267–278, 1984.
29. Z. Wang, “A fast algorithm for the discrete sine transform implemented by the fast cosine transform,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-30, pp. 814–815, 1982.
30. Z. Wang, “Fast algorithms for the discrete W transform and for the discrete Fourier transform,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, no. 4, 803–816, Aug. 1984.
31. S. Winograd, “On computing the discrete Fourier transform,” Math.Computation, vol. 32, no. 141, Jan. 1978.
32. K. L. Wong, R. Chan, D. P. K. Lun, and W. C. Siu, “Efficient address generation for prime factor algorithms,” IEEE Trans. Acoust., Speech Signal Processing, vol. 38, no. 9, 1518–1528, 1990.
33. K. L. Wong and W. C. Siu, “Fast address generation for the computation of prime factor algorithms,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, 1989, 1091–1094.
34. K. L. Wong and W. C. Siu, “Data routing networks for systolic/pipeline realization of prime factor mapping,” IEEE Trans. Comput., vol. 40, no. 9, 1072–1074, 1991.
35. P. P. N. Yang and M. J. Narasimha, “Prime factor decomposition of the discrete cosine transform,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, 1985, pp. 772–775.