Skip to main content
EURASIP Journal on Advances in Signal Processing
Download PDF
  • Research Article
  • Open access
  • Published:

Estimation of Spectral Exponent Parameter of Process in Additive White Background Noise

EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 063219 (2007) Cite this article

Abstract

An extension to the wavelet-based method for the estimation of the spectral exponent, , in a process and in the presence of additive white noise is proposed. The approach is based on eliminating the effect of white noise by a simple difference operation constructed on the wavelet spectrum. The parameter is estimated as the slope of a linear function. It is shown by simulations that the proposed method gives reliable results. Global positioning system (GPS) time-series noise is analyzed and the results provide experimental verification of the proposed method.

References

  1. Wornell GW:Wavelet-based representations for the family of fractal processes. Proceedings of the IEEE 1993,81(10):1428-1450. 10.1109/5.241506

    Article  Google Scholar 

  2. Agnew DC: The time-domain behavior of power-law noises. Geophysical Research Letters 1992,19(4):333-336. 10.1029/91GL02832

    Article  Google Scholar 

  3. Langbein J, Johnson H: Correlated errors in geodetic time series: implications for time-dependent deformation. Journal of Geophysical Research 1997,102(B1):591-604. 10.1029/96JB02945

    Article  Google Scholar 

  4. Mao A, Harrison CGA, Dixon TH: Noise in GPS coordinate time series. Journal of Geophysical Research 1999,104(B2):2797-2816. 10.1029/1998JB900033

    Article  Google Scholar 

  5. Williams SDP, Bock Y, Fang P, et al.: Error analysis of continuous GPS position time series. Journal of Geophysical Research 2004,109(B3):1-19.

    Article  Google Scholar 

  6. Leland WE, Taqqu MS, Willinger W, Wilson DV: On the self-similar nature of Ethernet traffic (extended version). IEEE/ACM Transactions on Networking 1994,2(1):1-15. 10.1109/90.282603

    Article  Google Scholar 

  7. Mandelbrot BB, van Ness JW: Fractional Brownian motions, fractional noises and applications. SIAM Review 1968,10(4):422-437. 10.1137/1010093

    Article  MathSciNet  Google Scholar 

  8. Wornell GW, Oppenheim AV: Estimation of fractal signals from noisy measurements using wavelets. IEEE Transactions on Signal Processing 1992,4(3):611-623.

    Article  Google Scholar 

  9. Ninness B:Estimation of noise. IEEE Transactions on Information Theory 1998,44(1):32-46. 10.1109/18.650986

    Article  MathSciNet  Google Scholar 

  10. Du L, Zhuang Y, Wu Y: noise separated from white noise with wavelet denoising. Microelectronics Reliability 2002,42(2):183-188. 10.1016/S0026-2714(01)00249-9

    Article  Google Scholar 

  11. Kaplan LM, Kuo C-CJ: Fractal estimation from noisy data via discrete fractional Gaussian noise (DFGN) and the Haar basis. IEEE Transactions on Signal Processing 1993,41(12):3554-3562. 10.1109/78.258096

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronics and Communications Engineering, Istanbul Technical University, Maslak, Istanbul, 34469, Turkey

    Süleyman Baykut & Tayfun Akgül

  2. TÜBİTAK Marmara Research Center, Earth and Marine Sciences Institute, Gebze, Kocaeli, 41470, Turkey

    Tayfun Akgül & Semih Ergintav

Authors
  1. Süleyman Baykut
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tayfun Akgül
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Semih Ergintav
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Süleyman Baykut.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://doi.org/creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Baykut, S., Akgül, T. & Ergintav, S. Estimation of Spectral Exponent Parameter of Process in Additive White Background Noise. EURASIP J. Adv. Signal Process. 2007, 063219 (2007). https://doi.org/10.1155/2007/63219

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/2007/63219

Keywords