Skip to main content
SpringerLink
Log in

Arbitrary-Length Jacket-Haar Transforms

  • Conference paper
  • First Online:
Algorithms and Architectures for Parallel Processing (ICA3PP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9529))

Abstract

Recently, motivated by Haar transform and Jacket transform, Jacket Haar transform has been successfully generalized, but unfortunately, it is not available in the case where the length N is not a power of 2. In this paper, with the new proposed generation methods, the arbitrary-length Jacket-Haar transform can be constructed capriciously. Meanwhile, just like the original Haar transform, the presented arbitrary-length Jacket-Haar transform has fast algorithm and can be decomposed into the 2-point generalized Haar transforms, the general form of which is also successfully derived. Subsequently, the proposed Jacket-Haar transform has been applied to the electrocardiogram (ECG) signal analysis, and simulation results show that the new proposed transform is more efficient than FFT in signal reconstruction.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Rao, K.R., Ahmed, N.: Orthogonal transforms for digital signal processing. IEEE Trans. Syst. Man Cybern. 35(1), 66–67 (1979)

    Google Scholar 

  2. Aung, A., Ng, B.P., Rahardja, S.: Sequency-ordered complex hadamard transform: properties, computational complexity and applications. IEEE Trans. Sig. Process. 56(8), 3562–3571 (2008)

    Article  MathSciNet  Google Scholar 

  3. Wu, J., Wang, L., Yang, G.: Sliding conjugate symmetric sequency-ordered complex hadamard transform: fast algorithm and applications. IEEE Trans. Circuits Syst. I 59(6), 1321–1334 (2012)

    Article  MathSciNet  Google Scholar 

  4. Pei, S.C., Wen, C.C., Ding, J.J.: Sequency-ordered generalized Walsh-Fourier transform. IEEE Trans. Sig. Process. 93(4), 828–841 (2013)

    Google Scholar 

  5. Lee, M.H.: The center weighted Hadamard transform. IEEE Trans. Circuits Syst. 36(9), 1247–1249 (1989)

    Article  Google Scholar 

  6. Lee, M.H., Rajan, B.S., Member, S.: A generalized reverse jacket transform. IEEE Trans. Circuits Syst. II 48(7), 684–690 (2001)

    Article  MATH  Google Scholar 

  7. Zeng, G.H., Lee, M.H.: A generalized reverse block jacket transform. IEEE Trans. Circuits Syst. I 55(6), 1589–1600 (2008)

    Article  MathSciNet  Google Scholar 

  8. Chen, Z., Lee, M.H., Song, W.: Arikan and alamouti matrices based on fast block-wise inverse jacket transform. EURASIP J. Adv. Sig. Proc. 37(4), 1247–1249 (2013)

    Google Scholar 

  9. Jiang, X., Lee, M.H., Guo, Y.: Ternary codes from modified Jacket matrices. J. Commun. Netw. 13(1), 12–16 (2011)

    Article  Google Scholar 

  10. Guo, Y., Lee, M.H., Kim, K.J.: An explicit construction of fast cocyclic jacket transform on the finite field with any size. J. Adv. Sig. Process. 1, 1–10 (2012)

    Article  Google Scholar 

  11. Lee, M.H., Khan, M.H.A., Kim, K.J.: A fast hybrid Jacket-Hadamard matrix based diagonal block-wise transform. Sig. Process. Image Commun. 29(1), 49–65 (2014)

    Article  Google Scholar 

  12. Ma, W.P.: The Jacket Matrix and Cryptography. Chonbuk National University, Chonju (2004)

    Google Scholar 

  13. Song, W., Lee, M.H., Matalgah, M.M.: Quasi-orthogonal space-time block codes designs based on Jacket transform. J. Commun. Netw. 3, 240–245 (2010)

    Article  Google Scholar 

  14. Shi, R., Guo, Y., Lee, M.H.: Quantum codes based on fast pauli block transforms in the finite field. Quantum Inf. Process. 9(5), 611–628 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Guo, Y., Liu, Y., Song, X.: A simple fast jacket transform for DFT based on generalized prime factor decomposing algorithm. In: IEEE Symposium on Business, Engineering and Industrial Applications, pp. 265–270 (2011)

    Google Scholar 

  16. Li, J., Yan, Y., Duan, W.: Tensor decomposition of Toeplitz Jacket matrices for big data processing. In: 2015 International Conference on Big Data and Smart Computing (BigComp), pp. 11–14. IEEE (2015)

    Google Scholar 

  17. Lee, M.H., Khan, M.H.A.: Big Data ‘Fork’: tensor product for DCT-II/DST-II/ DFT/HWT. In: IEEE International Symposium on Broadband Multimedia Systems and Broadcasting (BMSB), pp. 1–6. IEEE (2014)

    Google Scholar 

  18. Mao, Y., Peng, J., Guo, Y.: On the fast fractional Jacket transform. Circuits Syst. Sig. Process. 33(5), 1491–1505 (2014)

    Article  MathSciNet  Google Scholar 

  19. Lee, M.H., Zhang, X.D., Jiang, X.Q.: Fast parametric reciprocal-orthogonal jacket transforms. EURASIP J. Adv. Sig. Proc. 149 (2014)

    Google Scholar 

  20. Khan, M.H.A., Li, J., Lee, M.H.: A block diagonal jacket matrices for MIMO broadcast channels. In: IEEE International Symposium on Broadband Multimedia Systems and Broadcasting (BMSB), pp. 1–7. IEEE (2013)

    Google Scholar 

  21. Ding, J., Pei, S., Wu, P.: Jacket Haar transform. IEEE Int. Symp. Circuits Syst. 19(5), 1520–1523 (2011)

    Google Scholar 

  22. Ding, J., Pei, S., Wu, P.: Arbitrary-length Walsh-Jacket transforms. In: APSIPA Annual Summit and Conference, Xi’an, China (2011)

    Google Scholar 

Download references

Acknowledgment

This work was supported by the National Natural Science Foundation of China (61379153, 61272495), the New Century Excellent Talents in University, China (NCET-11-0510), and partly by the World Class University (R32-2010-000-20014-0), and Fundamental Research (2010-0020942, 2012-002521) NRF, Korea.

Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha, 410083, China

    Guibo Liu, Dayong Luo, Geli Lv & Ying Guo

  2. Institute of Information and Communication, Chonbuk National, Jeonju, 561-756, South Korea

    Moonho Lee

Authors
  1. Guibo Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dayong Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Geli Lv
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ying Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Moonho Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guibo Liu .

Editor information

Editors and Affiliations

  1. Central South University, Changsha, China

    Guojun Wang

  2. The University of Sydney, Sydney, New South Wales, Australia

    Albert Zomaya

  3. University of Murcia, Murcia, Murcia, Spain

    Gregorio Martinez

  4. Hunan University , Changsha, China

    Kenli Li

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Liu, G., Luo, D., Lv, G., Guo, Y., Lee, M. (2015). Arbitrary-Length Jacket-Haar Transforms. In: Wang, G., Zomaya, A., Martinez, G., Li, K. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2015. Lecture Notes in Computer Science(), vol 9529. Springer, Cham. https://doi.org/10.1007/978-3-319-27122-4_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-27122-4_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27121-7

  • Online ISBN: 978-3-319-27122-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation