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

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. 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

  2. 2.

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

  3. 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

  4. 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

  5. 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.

  6. 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

  7. 7.

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

  8. 8.

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

  9. 9.

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

  10. 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

  11. 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

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Correspondence to Süleyman Baykut.

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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.

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Keywords

  • Information Technology
  • Background Noise
  • Quantum Information
  • White Background
  • White Background Noise