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线性调频信号是工程中常见的一种信号, 由于其为非周期信号, 无法以频域信噪比作为衡量其是否产生随机共振的测量手段, 故鲜有文献研究以线性调频信号为激励信号的随机共振现象. 本文利用线性调频信号在最优分数阶Fourier变换域上的能量聚集性, 首次提出以最优分数阶Fourier变换域上定义的信噪比作为测量手段, 研究了线性调频信号叠加高斯白噪声激励过阻尼双稳系统的随机共振现象, 且发现了以线性调频信号为激励信号时产生的新现象, 即随着信号频率的增大, 随机共振将逐渐减弱, 并给出了合理的解释.仿真的结果与理论分析一致, 验证了本文所提出方法的有效性.
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关键词:
- 线性调频信号 /
- 分数阶Fourier变换 /
- 随机共振
It is improper to use frequency domain signal-to-noise ratio as a measure to judge whether stochastic resonance happens with chirp signal which is common in engineering. As a result, there is little literature on this subject. Using the energy aggregation in an optimal fractional Fourier transform domain of chirp signal, in this paper we propose a new signal-to-noise ratio defined in an optimal fractional domain to study the stochastic resonance of over-damped bistable system driven by chirp signal and Gaussian white noise. A new phenomenon is found, that is, the stochastic resonance phenomenon weakens gradually as the frequency of chirp signal increases. And it is reasonably explained in this paper. The consistency of simulation results with theoretical analysis verifies the effectiveness of the method proposed in this paper.-
Keywords:
- chirp signal /
- fractional Fourier transform /
- stochastic resonance
[1] Benzi R, Suter A, Vulpana A 1981 Physica A 14 L453
[2] Benzi R, Parisi G, Suter A, Vulpana A 1982 Tellus 34 11
[3] Gitterman M 2003 Phys. Rev. E 67 057103
[4] Jia Y, Yu S N, Li J R 2000 Phys. Rev. E 62 1869
[5] Berdichevsky V, Gitterman M 1996 Europhys. Lett. 36 161
[6] Luo X, Zhu S 2003 Phys. Rev. E 67 021104
[7] Collins J J, Chow C C, Imhoff T T 1995 Phys. Rev. E 52 3321
[8] Collins J J, Chow C C, Capela A C, Imhoff T T 1996 Phys. Rev. E 54 5575
[9] McNamara B, Wiesenfel K 1989 Phys. Rev. A 39 4854
[10] Tao R, Qin L, Wang Y 2004 Theory and Applications of the Fractional Fourier Transform (1st Ed.) (Beijing:Tsinghua University Press) p111 (in Chinese) [陶然, 齐林, 王越 2004 分数阶Fourier变换的原理与应用(第一版) (北京:清华大学出版社) 第111页]
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[1] Benzi R, Suter A, Vulpana A 1981 Physica A 14 L453
[2] Benzi R, Parisi G, Suter A, Vulpana A 1982 Tellus 34 11
[3] Gitterman M 2003 Phys. Rev. E 67 057103
[4] Jia Y, Yu S N, Li J R 2000 Phys. Rev. E 62 1869
[5] Berdichevsky V, Gitterman M 1996 Europhys. Lett. 36 161
[6] Luo X, Zhu S 2003 Phys. Rev. E 67 021104
[7] Collins J J, Chow C C, Imhoff T T 1995 Phys. Rev. E 52 3321
[8] Collins J J, Chow C C, Capela A C, Imhoff T T 1996 Phys. Rev. E 54 5575
[9] McNamara B, Wiesenfel K 1989 Phys. Rev. A 39 4854
[10] Tao R, Qin L, Wang Y 2004 Theory and Applications of the Fractional Fourier Transform (1st Ed.) (Beijing:Tsinghua University Press) p111 (in Chinese) [陶然, 齐林, 王越 2004 分数阶Fourier变换的原理与应用(第一版) (北京:清华大学出版社) 第111页]
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