中国物理B ›› 2017, Vol. 26 ›› Issue (10): 100508-100508.doi: 10.1088/1674-1056/26/10/100508

• SPECIAL TOPIC—Non-equilibrium phenomena in soft matters • 上一篇    下一篇

Extracting hidden weak sinusoidal signal with short duration from noisy data:Analytical theory and computational realization

Ying Zhang(张英), Zhaoyang Zhang(张朝阳), Hong Qian(钱弘), Gang Hu(胡岗)   

  1. 1. Department of Physics, Beijing Normal University, Beijing 100875, China;
    2. Faculty of Science, Ningbo University, Ningbo 315211, China;
    3. Department of Applied Mathematics, University Washington, Seattle, WA 98195, USA
  • 收稿日期:2017-08-04 修回日期:2017-08-25 出版日期:2017-10-05 发布日期:2017-10-05
  • 通讯作者: Gang Hu E-mail:ganghu@bnu.edu.cn
  • 基金资助:

    Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 11135001).

Extracting hidden weak sinusoidal signal with short duration from noisy data:Analytical theory and computational realization

Ying Zhang(张英)1, Zhaoyang Zhang(张朝阳)1,2, Hong Qian(钱弘)3, Gang Hu(胡岗)1   

  1. 1. Department of Physics, Beijing Normal University, Beijing 100875, China;
    2. Faculty of Science, Ningbo University, Ningbo 315211, China;
    3. Department of Applied Mathematics, University Washington, Seattle, WA 98195, USA
  • Received:2017-08-04 Revised:2017-08-25 Online:2017-10-05 Published:2017-10-05
  • Contact: Gang Hu E-mail:ganghu@bnu.edu.cn
  • Supported by:

    Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 11135001).

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摘要：

Signal detection is both a fundamental topic of data science and a great challenge for practical engineering. One of the canonical tasks widely investigated is detecting a sinusoidal signal of known frequency ω with time duration T:I(t)=Acos ω t+Γ(t), embedded within a stationary noisy data. The most direct, and also believed to be the most efficient, method is to compute the Fourier spectral power at ω:B=|2/T∫0T I(t)eiωtdt|. Whether one can out-perform the linear Fourier approach by any other nonlinear processing has attracted great interests but so far without a consensus. Neither a rigorous analytic theory has been offered. We revisit the problem of weak signal, strong noise, and finite data length T=O(1), and propose a signal detection method based on resonant filtering. While we show that the linear approach of resonant filters yield a same signal detection efficiency in the limit of T→∞, for finite time length T=O(1), our method can improve the signal detection due to the highly nonlinear interactions between various characteristics of a resonant filter in finite time with respect to transient evolution. At the optimal match between the input I(t), the control parameters, and the initial preparation of the filter state, its performance exceeds the above threshold B considerably. Our results are based on a rigorous analysis of Gaussian processes and the conclusions are supported by numerical computations.

关键词: signal detection, strong noise, stochastic theory, time series analysis

Abstract:

Signal detection is both a fundamental topic of data science and a great challenge for practical engineering. One of the canonical tasks widely investigated is detecting a sinusoidal signal of known frequency ω with time duration T:I(t)=Acos ω t+Γ(t), embedded within a stationary noisy data. The most direct, and also believed to be the most efficient, method is to compute the Fourier spectral power at ω:B=|2/T∫0T I(t)eiωtdt|. Whether one can out-perform the linear Fourier approach by any other nonlinear processing has attracted great interests but so far without a consensus. Neither a rigorous analytic theory has been offered. We revisit the problem of weak signal, strong noise, and finite data length T=O(1), and propose a signal detection method based on resonant filtering. While we show that the linear approach of resonant filters yield a same signal detection efficiency in the limit of T→∞, for finite time length T=O(1), our method can improve the signal detection due to the highly nonlinear interactions between various characteristics of a resonant filter in finite time with respect to transient evolution. At the optimal match between the input I(t), the control parameters, and the initial preparation of the filter state, its performance exceeds the above threshold B considerably. Our results are based on a rigorous analysis of Gaussian processes and the conclusions are supported by numerical computations.

Key words: signal detection, strong noise, stochastic theory, time series analysis

中图分类号:  (Stochastic analysis methods)

  • 05.10.Gg
05.45.Tp (Time series analysis) 02.50.-r (Probability theory, stochastic processes, and statistics)