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The frequency invariance and phase shift of the first-order steady state moment of system response are deduced for fractional order linear oscillator. Moreover, through the theoretical analysis, the amplification effect of fractional order linear system on the amplitude of first-order steady state moment is verified in stochastic resonance mechanism. Duffing detector is used to realize weak signal detection based on parameter perturbation sensitivity and noise immunity of chaos. Numerical simulations show that this scheme can effectively extract the weak sinusoidal signal from the strong colored noise background and significantly reduce the signal-to-noise ratio threshold in comparison with traditional chaotic detection method.
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Keywords:
- weak signal detection /
- stochastic resonance /
- chaos /
- fractional order
[1] Wang G Y, Zheng W, He S 2002 Signal Processing 82 103
[2] Li Y, Lu P, Yang B J, Zhao X P 2006 Acta Phys. Sin. 55 1672 (in Chinese) [李月, 路鹏, 杨宝俊, 赵雪平 2006 物理学报 55 1672]
[3] Li Y, Xu K, Yang B J, Yuan Y, Wu N 2008 Acta Phys. Sin. 57 3353 (in Chinese) [李月, 徐凯, 杨宝俊, 袁野, 吴宁 2008 物理学报 57 3353]
[4] Li Y, Yang B J, Du L Z 2003 Chin. Phys. 12 714
[5] Benzi R, Sutera A, Vulpiana A 1981 J. Phys. A 14 L453
[6] Soika E K, Mankin R, Ainsaar A 2010 Phys. Rev. E 81 011141
[7] Jin Y F, Xu W, Li W, Xu M 2005 Acta Phys. Sin. 54 2562 (in Chinese) [靳艳飞, 徐伟, 李伟, 徐猛 2005 物理学报 54 2562]
[8] Ning L J, Xu W 2009 Acta Phys. Sin. 58 2889 (in Chinese) [宁丽娟, 徐伟 2009 物理学报 58 2889]
[9] Gitterman M 2005 Physica A 352 309
[10] Zhou C S, Lai C H 1999 Phys. Rev. E 60 3928
[11] Du L C, Mei D C 2011 Phys. Scr. 84 015003
[12] Shapiro V E, Loginov V M 1978 Physica A 91 563
[13] Hu G, Nicolis G, Nicolis C 1990 Phys. Rev. A 42 2030
[14] Petracchi D, Gebeshuber L C, DeFelice L J 2000 Chaos, Solitons and Fractals 11 1819
[15] Sauga A, Mankin R, Ainsaar A 2010 Wseas Transactions on Systems 9 1021
[16] Li Y, Yang B J, Shi Y W 2003 Acta Phys. Sin. 52 526 (in Chinese) [李月, 杨宝俊, 石要武 2003 物理学报 52 526]
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[1] Wang G Y, Zheng W, He S 2002 Signal Processing 82 103
[2] Li Y, Lu P, Yang B J, Zhao X P 2006 Acta Phys. Sin. 55 1672 (in Chinese) [李月, 路鹏, 杨宝俊, 赵雪平 2006 物理学报 55 1672]
[3] Li Y, Xu K, Yang B J, Yuan Y, Wu N 2008 Acta Phys. Sin. 57 3353 (in Chinese) [李月, 徐凯, 杨宝俊, 袁野, 吴宁 2008 物理学报 57 3353]
[4] Li Y, Yang B J, Du L Z 2003 Chin. Phys. 12 714
[5] Benzi R, Sutera A, Vulpiana A 1981 J. Phys. A 14 L453
[6] Soika E K, Mankin R, Ainsaar A 2010 Phys. Rev. E 81 011141
[7] Jin Y F, Xu W, Li W, Xu M 2005 Acta Phys. Sin. 54 2562 (in Chinese) [靳艳飞, 徐伟, 李伟, 徐猛 2005 物理学报 54 2562]
[8] Ning L J, Xu W 2009 Acta Phys. Sin. 58 2889 (in Chinese) [宁丽娟, 徐伟 2009 物理学报 58 2889]
[9] Gitterman M 2005 Physica A 352 309
[10] Zhou C S, Lai C H 1999 Phys. Rev. E 60 3928
[11] Du L C, Mei D C 2011 Phys. Scr. 84 015003
[12] Shapiro V E, Loginov V M 1978 Physica A 91 563
[13] Hu G, Nicolis G, Nicolis C 1990 Phys. Rev. A 42 2030
[14] Petracchi D, Gebeshuber L C, DeFelice L J 2000 Chaos, Solitons and Fractals 11 1819
[15] Sauga A, Mankin R, Ainsaar A 2010 Wseas Transactions on Systems 9 1021
[16] Li Y, Yang B J, Shi Y W 2003 Acta Phys. Sin. 52 526 (in Chinese) [李月, 杨宝俊, 石要武 2003 物理学报 52 526]
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