Abstract
In this paper, those splendid characters of the Hilbert transform let the processes that taking wavelet transform after taking Hilbert transform for the statistic self-similarity processes FBM [B H (t)] become another processes, that firstly taking Hilbert transform for the wavelet function ϕ(t) and forming a new wavelet function ψ(t), secondly taking the wavelet transform for B H (t). Then, we use the optimum threshold to estimate the \( \hat B_H (t) \) embedded in additive white noise. Typical computer simulation results to demonstrate the viability and the effectiveness of the Hilbert transform in the signal’s estimation of the statistic self-similarity process.
Supported by the NNSF of china (No. 19971063)
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References
B. S. Chen and G. W. Lin, “Multiscale Wiener filter for the restoration of fractal signals: Wavelet filter bank approach”, IEEE Trans. Signal Processing, Vol. 42, No. 11, PP. 2972–2982, 1994.
B. S. Chen and W. S. Hou, “Deconvolution filter design for fractal signal transmission systems: A multiscale Kalman filter bank approach”, IEEE Trans. Signal Processing, Vol. 45, PP. 1395–1364, 1997.
P. Flandrin, “On the spectrum of fractional Brownian motion”, IEEE Trans. Information Theotry, Vol. 35, No. 1, PP. 197–199, 1989.
P. Flandrin, “Wavelet analysis and synthesis of fractional Brownian motion”, IEEE Trans. Information Theory, Vol. 38, No. 2, PP. 910–917, 1992.
B. B. Mandelbrot and J. W. Van Ness, “Fractional Browrian motions, fractonal motions, fractional noises and applications” SIAM Rev., Vol. 10. No. 4, pp. 422–437, 1968.
G. W. Wornell, “A Karhunen-Loeve-Like Expansion for 1/f Processes Via Wavelets”, IEEE Trans, Information Theoty, V0l. 36, No. 4, PP. 859–861, 1990.
Hong Ma, Michio Umeda, Wei Su, “Hilbert Transform of Non-stationary Stochastic Signal and Parameter Estimation”, to appear.
Kesu Zhang, Hong Ma, Zhisheng You, Michio Umeda, “Wavelet Estimation of Non-stationary Fractal Stochastic Signals Using Optimum Threshold Technique”, to appear.
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© 2001 Springer-Verlag Berlin Heidelberg
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Su, W., Ma, H., Tang, Y.Y., Umeda, M. (2001). Wavelet Transform Method of Waveform Estimation for Hilbert Transform of Fractional Stochastic Signals with Noise. In: Tang, Y.Y., Yuen, P.C., Li, Ch., Wickerhauser, V. (eds) Wavelet Analysis and Its Applications. WAA 2001. Lecture Notes in Computer Science, vol 2251. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45333-4_36
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DOI: https://doi.org/10.1007/3-540-45333-4_36
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