Skip to main content
SpringerLink
Log in

Combined Polynomial Transform and Radix-q Algorithm for Multi-dimensional DCT-III

  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

By combining the polynomial transform and radix-q decomposition, the paper presents a new algorithm for the type-III r-dimensional discrete Cosine transform (rD-DCT-III) with size q l 1×q l 2× ... ×q l r , where q is an odd prime number. The number of multiplications for computing an rD-DCT-III is approximately 1/r times that needed by the row-column method while the number of additions increase slightly. The total number of operations (additions plus multiplications) is also reduced. The proposed algorithm has a simple computational structure because it needs only 1D-DCT-III and the polynomial transform.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. P. Apousleman, M. W. Marcellin and B. R. Hunt, ''Compression of Hyperspectral Imagery Using the 3-D DCT and Hybrid DPCM/DCT,'' IEEE Trans. Geoscience and Remote Sensing, vol. 33, no. 1, pp. 26-34, 1995.

    Google Scholar 

  2. G. Bi, ''Fast Algorithms for Type-III DCT of Composite Sequence Lengths,'' IEEE Trans. Signal Processing, vol. 47, pp. 2053-2059, July 1999.

    Google Scholar 

  3. G. Bi, G. Li, K. K. Ma and T. C. Tan, ''On the Computation of Two-Dimensional DCT,'' IEEE Trans. Signal Processing, vol. 48, pp. 1171-1183, April 2000.

    Google Scholar 

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

    Google Scholar 

  5. S. C. Chan and K. L. Ho, ''Fast Algorithm for Computing the Discrete Cosine Transform,'' IEEE Trans. Circuits Syst. II, vol. 39, pp. 185-190, Mar. 1992.

    Google Scholar 

  6. Y. H. Chan and W. C. Siu, ''Mixed-Radix Discrete Cosine Transform,'' IEEE Trans. Signal Processing, vol. 41, pp. 3157-3161, Nov. 1993.

    Google Scholar 

  7. N. I. Cho and S. U. Lee, ''Fast Algorithm and Implementation for 2-D Discrete Cosine Transform,'' IEEE Trans. Circuits and Systems, vol. 38, no. 3, pp. 297-305, 1991.

    Google Scholar 

  8. P. Duhamel and C. Guillemot, ''Polynomial Transform Computation of the 2-D DCT,'' Proc. ICASSP, pp. 1515-1518, 1990.

  9. 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, pp. 25-33, FEB. 1999.

    Google Scholar 

  10. E. Feig and S. Winograd, ''Fast Algorithm for the Discrete Cosine Transform,'' IEEE Trans. Signal Processing, vol. 40, no. 9, pp. 2174-2193, 1992.

    Google Scholar 

  11. Y. M. Huang and J. L. Wu, ''A Refined Fast 2-D Discrete Cosine Transform Algorithm,'' IEEE Trans. Signal Processing, vol. 47, no. 3, pp. 904-907, 1999.

    Google Scholar 

  12. Z. R. Jiang and Y. H. Zeng, Polynomial Transform and its Applications, P.R. China: National University of Defense Technology Press, 1989 (in Chinese).

    Google Scholar 

  13. Z. R. Jiang, Y. H. Zeng and P. N. Yu, Fast Algorithms, Changsha, P.R.China: National University of Defense Technology Press, 1994 (in Chinese).

    Google Scholar 

  14. D. C. Kar and V. V. Rao, ''On the Prime Factor Decomposition Algorithm for the Discrete Sine Transform,'' IEEE. Trans. Signal Processing, vol. 42, pp. 3258-3260, Nov. 1994.

    Google Scholar 

  15. B. G. Lee, ''A New Algorithm to Compute the Discrete Cosine Transform,'' IEEE Trans. Acoust., Speech, Signal Processing, vol. 32, pp. 1243-1245, 1984.

    Google Scholar 

  16. P. Lee and F. Y. Huang, ''An Efficient Prime-Factor Algorithm for the Discrete Cosine Transform and its Hardware Implementations,'' IEEE. Trans. Signal Processing, vol. 42, pp. 2041-2058, 1994.

    Google Scholar 

  17. J. Prado and P. Duhamel, ''A Polynomial Transform Based Computation of the 2-D DCT with Minimum Multiplicative Complexity,'' Proc. ICASSP, vol. 3, pp. 1347-1350, 1996.

    Google Scholar 

  18. Y. L. Siu and W.C. Siu, ''Variable Temporal-Length 3-D Discrete Cosine Transform Coding,'' IEEE Trans. Image Processing, vol. 6, no. 5, pp. 758-763, 1997.

    Google Scholar 

  19. Z. S. Wang, Z. Y. He, C. R. Zhou 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 and Systems-II: Analog and Digital Signal processing, vol. 46, no. 5, pp. 617-627, 1999.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of EEE, Nanyang Technological University, Singapore

    Yonghong Zeng (Research fellow)

  2. National University of Defense Technology, P.R. China

    Yonghong Zeng (Research fellow), Guoan Bi & Zhiping Lin

Authors
  1. Yonghong Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guoan Bi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhiping Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zeng, Y., Bi, G. & Lin, Z. Combined Polynomial Transform and Radix-q Algorithm for Multi-dimensional DCT-III. Multidimensional Systems and Signal Processing 13, 79–99 (2002). https://doi.org/10.1023/A:1013895428361

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1013895428361

Search

Navigation