Open Access

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

EURASIP Journal on Advances in Signal Processing20072007:063219

Received: 29 September 2006

Accepted: 29 April 2007

Published: 17 June 2007


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.


Authors’ Affiliations

Department of Electronics and Communications Engineering, Istanbul Technical University
TÜBİTAK Marmara Research Center, Earth and Marine Sciences Institute


  1. Wornell GW:Wavelet-based representations for the family of fractal processes. Proceedings of the IEEE 1993,81(10):1428-1450. 10.1109/5.241506View ArticleGoogle Scholar
  2. Agnew DC: The time-domain behavior of power-law noises. Geophysical Research Letters 1992,19(4):333-336. 10.1029/91GL02832View ArticleGoogle 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. 10.1029/96JB02945View ArticleGoogle Scholar
  4. Mao A, Harrison CGA, Dixon TH: Noise in GPS coordinate time series. Journal of Geophysical Research 1999,104(B2):2797-2816. 10.1029/1998JB900033View ArticleGoogle 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.View ArticleGoogle 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. 10.1109/90.282603View ArticleGoogle Scholar
  7. Mandelbrot BB, van Ness JW: Fractional Brownian motions, fractional noises and applications. SIAM Review 1968,10(4):422-437. 10.1137/1010093MathSciNetView ArticleMATHGoogle 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.View ArticleGoogle Scholar
  9. Ninness B:Estimation of noise. IEEE Transactions on Information Theory 1998,44(1):32-46. 10.1109/18.650986MathSciNetView ArticleMATHGoogle 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)00249-9View ArticleGoogle 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. 10.1109/78.258096View ArticleMATHGoogle Scholar


© Süleyman Baykut et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.