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In this paper, a new detecting method for weak periodic signals with unknown periods and unknown forms, the so-called fractional stopping oscillation method, is presented. This new detecting method, which is based on the research of some dissipative system of single degree of freedom, is sensitive to periodic signal—even with unknown period and unknown form—and insensitive to noise. Compared with the known chaotic detections in which a built-in signal must be pre-set with the same frequency and the same form as the detected periodic signal, the fractional stopping oscillation method can not only be used even at lower SNR than chaotic detection, but also has some other notable advantages as follows: (1) it need not get the period and the form of detected signal before hand or pre-estimate them; (2) it need not pre-calculate the chaotic threshold value; (3) the existence of periodic signal in system input can be reliably and quantitatively judged by volatility index function, designed in this paper, for stopping oscillation method; (4) a more sensitive detection method can be achieved by the fractionalization of the detection system, especially, the detection threshold can reach -182 dB when the background noise is colored Gaussian noise.
[1] Proakis J G 2003 Digital Communications (4th Edition) (Beijing: Electronic Industry Press) p169
[2] Li Y, Yang B J 2004 Introduction of Detection by Chaotic Oscillator (Beijing: Electronic Industry Press) p55 (in Chinese) [李月, 杨宝俊 2004 混沌振子检测引论 (北京: 电子工业出版社) 第55页]
[3] Wang G Y 2001 IEEE Transaction on Industrial Electronics 46 440
[4] Wang Y S, Jiang W Z, Zhao J J, Fan H D 2008 Acta Phys. Sin. 57 2053 (in Chinese) [王永生, 姜文志, 赵建, 范洪达 2008 物理学报 57 2053]
[5] Wang J X, Hou C L 2010 International Conference on e-Education, e-Business, e-Management, e-Learning Sanya, Jan, 2010 p387
[6] Zhang Z F, Ding T R, Huang W Z, Dong Z X 1997 Qualitative Theory of Differential Equation (2nd Edition) (Beijing: Science Press) p450 (in Chinese) [张芷芬, 丁同仁, 黄文灶, 董镇喜 1997 微分方程的定性理论(第2版) (北京: 科学出版社) 第450页]
[7] Zhao P D, Zhang X D 2008 Acta Phys. Sin. 58 2791 (in Chinese) [赵品栋, 张晓丹 2008 物理学报 58 2791 ]
[8] Wang M J, Wang X Y 2010 Acta Phys. Sin. 59 1583 (in Chinese) [王明军, 王兴元 2010 物理学报 59 1583]
[9] Petráš I 2011 Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation (Beijing: Higher Education Press) p55
[10] Zhou S, Fu J L, Liu Y S 2010 Chin. Phys. B 19 120301
[11] Zhang Y 2012 Chin. Phys. B 21 084502
[12] Wei H Y, Xia T C 2012 Chin. Phys. B 21 100505
[13] Zhang S H, Chen B Y, Fu J L 2012 Chin. Phys. B 21 100202
[14] Chen X R 2000 Probability and Statistics (Beijing: Science Press) p141 (in Chinese) [陈希孺 2000 概率论与数理统计(北京:科学出版社) 第141页]
[15] Zhu W Q 2003 Nonlinear Stochastic Dynamical Systems and Control p122 (in Chinese) [朱卫秋 2003 非线性随机动力系统与控制(北京: 科学出版社) 第122页]
[16] Arnold V I 1961 Sov. Math. Dokl. 2 247
[17] Tavazoei M S, Haeri M 2007 Phys. Lett. A 367 102
[18] Tavazoei M S, Haeri M 2008 Nonlinear Analysis 69 1299
[19] Tavazoei M S, Haeri M 2010 Automatic 46 94
[20] Wang Z H, Hu H Y 2010 Science China: Physics, Mechanics {& Astronomy} 53 345
[21] Sabattier J, Moze M, Farges C 2010 Comput. Math. Appl. 59 1594
[22] Tavazoei M S, Haeri M 2008 Physica D 237 2628
[23] Tavazoei M S, Haeri M 2009 Math. Comput. Simul. 79 1566
[24] Podlubny I 1999 Fractional Differential Equations (San Diego USA: Acadamic Press) p78
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[1] Proakis J G 2003 Digital Communications (4th Edition) (Beijing: Electronic Industry Press) p169
[2] Li Y, Yang B J 2004 Introduction of Detection by Chaotic Oscillator (Beijing: Electronic Industry Press) p55 (in Chinese) [李月, 杨宝俊 2004 混沌振子检测引论 (北京: 电子工业出版社) 第55页]
[3] Wang G Y 2001 IEEE Transaction on Industrial Electronics 46 440
[4] Wang Y S, Jiang W Z, Zhao J J, Fan H D 2008 Acta Phys. Sin. 57 2053 (in Chinese) [王永生, 姜文志, 赵建, 范洪达 2008 物理学报 57 2053]
[5] Wang J X, Hou C L 2010 International Conference on e-Education, e-Business, e-Management, e-Learning Sanya, Jan, 2010 p387
[6] Zhang Z F, Ding T R, Huang W Z, Dong Z X 1997 Qualitative Theory of Differential Equation (2nd Edition) (Beijing: Science Press) p450 (in Chinese) [张芷芬, 丁同仁, 黄文灶, 董镇喜 1997 微分方程的定性理论(第2版) (北京: 科学出版社) 第450页]
[7] Zhao P D, Zhang X D 2008 Acta Phys. Sin. 58 2791 (in Chinese) [赵品栋, 张晓丹 2008 物理学报 58 2791 ]
[8] Wang M J, Wang X Y 2010 Acta Phys. Sin. 59 1583 (in Chinese) [王明军, 王兴元 2010 物理学报 59 1583]
[9] Petráš I 2011 Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation (Beijing: Higher Education Press) p55
[10] Zhou S, Fu J L, Liu Y S 2010 Chin. Phys. B 19 120301
[11] Zhang Y 2012 Chin. Phys. B 21 084502
[12] Wei H Y, Xia T C 2012 Chin. Phys. B 21 100505
[13] Zhang S H, Chen B Y, Fu J L 2012 Chin. Phys. B 21 100202
[14] Chen X R 2000 Probability and Statistics (Beijing: Science Press) p141 (in Chinese) [陈希孺 2000 概率论与数理统计(北京:科学出版社) 第141页]
[15] Zhu W Q 2003 Nonlinear Stochastic Dynamical Systems and Control p122 (in Chinese) [朱卫秋 2003 非线性随机动力系统与控制(北京: 科学出版社) 第122页]
[16] Arnold V I 1961 Sov. Math. Dokl. 2 247
[17] Tavazoei M S, Haeri M 2007 Phys. Lett. A 367 102
[18] Tavazoei M S, Haeri M 2008 Nonlinear Analysis 69 1299
[19] Tavazoei M S, Haeri M 2010 Automatic 46 94
[20] Wang Z H, Hu H Y 2010 Science China: Physics, Mechanics {& Astronomy} 53 345
[21] Sabattier J, Moze M, Farges C 2010 Comput. Math. Appl. 59 1594
[22] Tavazoei M S, Haeri M 2008 Physica D 237 2628
[23] Tavazoei M S, Haeri M 2009 Math. Comput. Simul. 79 1566
[24] Podlubny I 1999 Fractional Differential Equations (San Diego USA: Acadamic Press) p78
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