Time series denoising with wavelet transform

• Autorzy: Kozłowski B.
• Języki publikacji: EN

Abstrakty

EN

This paper concerns the possibilities of applying wavelet analysis to discovering and reducing distortions occurring in time series. Wavelet analysis basics are briefly reviewed. WaveShrink method including three most common shrinking variants (hard, soft, and non-negative garrote shrinkage functions) is described. Another wavelet-based filtering method, with parameters depending on the length of wavelets, is introduced. Sample results of filtering follow the descriptions of both methods. Additionally the results of the use of both filtering methods are compared. Examples in this paper deal only with the simplest "mother" wavelet function - Haar basic wavelet function.

Słowa kluczowe

EN

wavelet transform; WaveShrink; filtration; noise reduction; Haar basic wavelet function

• Wydawca: Instytut Łączności - Państwowy Instytut Badawczy
• Czasopismo: Journal of Telecommunications and Information Technology
• Rocznik: 2005
• Tom: nr 3
• Strony: 91--95
• Opis fizyczny: Bibliogr.11 poz., il.

Twórcy

autor

Kozłowski B.

• Institute of Control and Computation Engineering, Warsaw University of Technology Nowowiejska st 15/19, 00-665 Warsaw, Poland,

Bibliografia

• [1] I. Daubechies, Ten Lectures on Wavelets. Philadelphia: SIAM, 1992.
• [2] D. L. Donoho and I. M. Johnstone, “Attempting to unknown smoothness via wavelet shrinkage”, Ann. Stat., vol. 90, pp. 1200–1224, 1998.
• [3] A. Haar, “Zur Theorie der orthogonalen Funktionensysteme”, Math. Ann., vol. LXIX, pp. 331–371, 1910.
• [4] B. Kozłowski, “Wavelet-based approach to time series denoising”, in Proc. Int. Conf. Decis. Supp. Telecommun. Inform. Soc. DSTIS, Warsaw, Poland, 2004, vol. 4, pp. 175–193.
• [5] B. Kozłowski, “On time series forecasting methods of linear complexity utilizing wavelets”, in Conf. Adv. Intell. Syst. – Theory Appl., Coop. IEEE Comput. Soc., Kirchberg, Luxembourg, 2004.
• [6] T. Li, Q. Li, S. Zhu, and M. Ogihara, “Survey on wavelet applications in data mining”, SIGKDD Expl., vol. 4, no. 2, pp. 49–68, 2003.
• [7] S. Mallat, A Wavelet Tour of Signal Processing. New York: Academic Press, 1998.
• [8] J. Morlet and A. Grossman, “Decomposition of hardy functions into square integrable wavelets of constant shape”, SIAM J. Math. Anal., vol. 15, no. 4 pp. 723–736, 1984.
• [9] D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis. Cambridge: Cambridge University Press, 2000.
• [10] L. Prasad and S. S. Iyengar, Wavelet Analysis with Applications to Image Processing. Boca Raton: CRC Press, 1997.
• [11] P. Yu, A. Goldberg, and Z. Bi, “Time series forecasting using wavelets with predictor-corrector boundary treatment”, in 7th ACM SIGKDD Int. Conf. Knowl. Discov. Data Min., San Francisco, USA, 2001.