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Wavelet Transform Method of Waveform Estimation for Hilbert Transform of Fractional Stochastic Signals with Noise

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Wavelet Analysis and Its Applications (WAA 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2251))

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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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Author information

Authors and Affiliations

  1. Dept of Mathematics, Sichuan University, 610064, Chengdu, China

    Wei Su & Hong Ma

  2. Dept of Computer Science, Hong Kong Baptist University, Kowloon Tong, HongKong

    Yuan Yan Tang

  3. Dept of Information Engineering, Osaka Electro-Communication University, Osaka, Japan

    Michio Umeda

Authors
  1. Wei Su
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  2. Hong Ma
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  3. Yuan Yan Tang
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  4. Michio Umeda
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Yuan Y. Tang , Pong C. Yuen  & Chun-hung Li ,  & 

  2. Department of Mathematics, Washington University, Cupples I, Campus Box 1146, 63130, St. Louis, Missouri, USA

    Victor Wickerhauser

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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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43034-6

  • Online ISBN: 978-3-540-45333-8

  • eBook Packages: Springer Book Archive

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