Skip to main content
SpringerLink
Log in

Orthogonal Residue Sequences

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

This paper presents a class of random orthogonal sequences associated with the number theoretic Hilbert transform. We present a constructive procedure for finding the random sequences for different modulus values. These random sequences have autocorrelation function that is zero everywhere excepting at the origin. These sequences may be used as keys in communication applications in a manner that is analogous to the use of PN sequences in spread spectrum systems.

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

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. R. Al-Aifari, A. Katsevich, Spectral analysis of the truncated Hilbert transform with overlap (2013) http://arxiv.org/abs/1302.6295

  2. M.R. Arinson et al., Using the Hilbert transform for 3D visualization of differential interference contrast microscope images. Journal of Microscopy 199, 79–84 (2000)

    Article  Google Scholar 

  3. A. Fuster, L.J. Garcia, An efficient algorithm to generate binary sequences for cryptographic purposes. Theor. Comput. Sci. 259, 679–688 (2001)

    Article  MATH  Google Scholar 

  4. N.S. Jayant, S. Kak, Uniform permutation privacy system, US Patent No. 4,100, 374, July 11, (1978)

  5. S. Kak, The discrete Hilbert transform. Proc. IEEE 58, 585–586 (1970)

    Article  Google Scholar 

  6. S. Kak, N.S. Jayant, Speech encryption using waveform scrambling. Bell Syst. Tech. J. 56, 781–808 (1977)

    Article  Google Scholar 

  7. S. Kak, Hilbert transformation for discrete data. Int. J. Electron. 34, 177–183 (1973)

    Article  MathSciNet  Google Scholar 

  8. S. Kak, The discrete finite Hilbert transform. Indian J. Pure Appl. Math. 8, 1385–1390 (1977)

    MATH  MathSciNet  Google Scholar 

  9. S. Kak, Multilayered array computing. Inf. Sci. 45, 347–365 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  10. S. Kak, A two-layered mesh array for matrix multiplication. Parallel Comput. 6, 383–385 (1988)

    Article  MATH  Google Scholar 

  11. S. Kak, The number theoretic Hilbert transform. Circuits Syst. Signal Process. 33, 2539–2548 (2014)

    Article  MathSciNet  Google Scholar 

  12. R. Kandregula, The basic discrete Hilbert transform with an information hiding application. (2009) http://arxiv.org/abs/0907.4176

  13. F.W. King, Hilbert Transforms (Cambridge University Press, Cambridge, 2009)

    Book  Google Scholar 

  14. V.K. Kotagiri, New results on the number theoretic Hilbert transform. (2013) http://arxiv.org/abs/1310.6924

  15. I. Noda, Determination of two-dimensional correlation spectra using the Hilbert transform. Appl. Spectrosc. 54, 994–999 (2000)

    Article  Google Scholar 

  16. S.K. Padala, K.M.M. Prabhu, Systolic arrays for the discrete Hilbert transform. Circuits Devices Syst. IEE Proc. 144, 259–264 (1997)

    Article  Google Scholar 

  17. I.G. Roy, On robust estimation of discrete Hilbert transform of noisy data. Geophysics 78, 239–249 (2013)

    Article  Google Scholar 

  18. A.J. Viterbi, CDMA: Principles of Spread Spectrum Communication (Prentice Hall, Upper Saddle River, NJ, 1995)

    MATH  Google Scholar 

  19. X. Wang, Y. Wu, B. Caron, Transmitter identification using embedded pseudo random sequences. IEEE Trans. Broadcast. 50, 244–252 (2004)

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported in part by the National Science Foundation Grant CNS-1117068.

Author information

Authors and Affiliations

  1. School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, OK, 74078, USA

    Subhash Kak

Authors
  1. Subhash Kak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Subhash Kak.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kak, S. Orthogonal Residue Sequences. Circuits Syst Signal Process 34, 1017–1025 (2015). https://doi.org/10.1007/s00034-014-9879-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-014-9879-1

Keywords

Search

Navigation