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In the parameter optimization issue of nonlinear adaptive denoising algorithm for chaotic signals, the window length is affected by different factors. In this paper, a criterion is proposed for selecting the optimal window length. According to the difference in autocorrelation function between chaotic signal and noise, first, the different window sizes are used for denoising noisy chaotic signals. Then, the residual autocorrelation degree (RAD) of each window length is computed. Finally, the optimal window length is obtained by shrinking the window length corresponding to the minimum RAD. Simulation results show that this criterion can automatically optimize the window length efficiently under different conditions, which improves the adaptivity of the denoising algorithm of chaotic signals.
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Keywords:
- chaos /
- denoising /
- adaptive filtering /
- correlation function
[1] L J H, Lu J A, Chen S H 2002 The Analysis and Applications of Chaotic Time Series (Wuhan: Wuhan University Press) pp1-8 (in Chinese) [吕金虎, 陆君安, 陈士华 2002 混沌时间序列分析及其应用 (武汉: 武汉大学出版社)第1–8页]
[2] Lorenz E N 1963 J. Atmos. Sci. 20 130
[3] Han M, Xu M L 2013 Acta Phys. Sin. 62 120510 (in Chinese) [韩敏, 许美玲 2013 62 120510]
[4] Sun J W, Shen Y, Yin Q, Xu C J 2013 Chaos 23 013140
[5] Wang X Y, Zhang N, Ren X L, Zhang Y L 2011 Chin. Phys. B 20 020507
[6] Xing H Y, Zhu Q Q, Xu W 2014 Acta Phys. Sin. 63 100505 (in Chinese) [行鸿彦, 朱清清, 徐伟 2014 63 100505]
[7] Wang X Y, Liu L T 2013 Chin. Phys. B 22 050503
[8] Wang X Y, Bao X M 2013 Chin. Phys. B 22 050508
[9] Urbanowicz K, Hołyst J A 2003 Phys. Rev. E 67 046218
[10] Feng J C 2012 Chaotic Signals and Information Processing (Beijing: Tsinghua University Press) pp32-35 (in Chinese) [冯久超 2012 混沌信号与信息处理(北京: 清华大学出版社)第32–35页]
[11] Badii R, Broggi G, Derighetti B, Ravani M 1988 Phys. Rev. Lett. 60 979
[12] Tung W W, Gao J B, Hu J, Yang L 2011 Phys. Rev. E 83 046210
[13] Gao J B, Sultan H, Hu J, Tung W W 2010 IEEE Signal Proc. Lett. 17 237
[14] Donoho D L 1995 IEEE Trans. Inform. Theory 41 613
[15] Han M, Liu Y H, Xi J H, Guo W 2007 IEEE Signal Proc. Lett. 14 62
[16] Cawley R, Hsu G H 1992 Phys. Rev. A 46 3057
[17] Schreiber T, Richter M 1999 Int. J. Bifurcation Chaos 9 2039
[18] Kopsinis Y, McLaughlin S 2009 IEEE Trans. Signal Proc. 57 1351
[19] Wang W B, Zhang X D, Wang X L 2013 Acta Phys. Sin. 62 050201 (in Chinese) [王文波, 张晓东, 汪祥莉 2013 62 050201]
[20] Feng J C 2005 Chin. Phys. Lett. 22 1851
[21] Arasaratnam I, Haykin S, Hurd T R 2010 IEEE Trans. Signal Proc. 58 4977
[22] Curtis F, Patrick O (translated by L S J) 2006 Applied Numerical Analysis (Beijing: China Machine Press) pp164-166 (in Chinese) [柯蒂斯F, 帕特里克O 著(吕淑娟 译) 2006 应用数值分析(北京: 机械工业出版社)第164–166页]
[23] Schafer R W 2011 IEEE Signal Proc. Mag. 28 111
[24] Savitzky A, Golay M J E 1964 Anal. Chem. 36 1627
[25] Krishnan S R, Seelamantula C S 2013 IEEE Trans. Signal Proc. 61 380
[26] Vivó-Truyols G, Schoenmakers P J 2006 Anal. Chem. 78 4598
[27] Chen G R, Ueta T 1999 Int. J. Bifurcation Chaos 9 1465
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[1] L J H, Lu J A, Chen S H 2002 The Analysis and Applications of Chaotic Time Series (Wuhan: Wuhan University Press) pp1-8 (in Chinese) [吕金虎, 陆君安, 陈士华 2002 混沌时间序列分析及其应用 (武汉: 武汉大学出版社)第1–8页]
[2] Lorenz E N 1963 J. Atmos. Sci. 20 130
[3] Han M, Xu M L 2013 Acta Phys. Sin. 62 120510 (in Chinese) [韩敏, 许美玲 2013 62 120510]
[4] Sun J W, Shen Y, Yin Q, Xu C J 2013 Chaos 23 013140
[5] Wang X Y, Zhang N, Ren X L, Zhang Y L 2011 Chin. Phys. B 20 020507
[6] Xing H Y, Zhu Q Q, Xu W 2014 Acta Phys. Sin. 63 100505 (in Chinese) [行鸿彦, 朱清清, 徐伟 2014 63 100505]
[7] Wang X Y, Liu L T 2013 Chin. Phys. B 22 050503
[8] Wang X Y, Bao X M 2013 Chin. Phys. B 22 050508
[9] Urbanowicz K, Hołyst J A 2003 Phys. Rev. E 67 046218
[10] Feng J C 2012 Chaotic Signals and Information Processing (Beijing: Tsinghua University Press) pp32-35 (in Chinese) [冯久超 2012 混沌信号与信息处理(北京: 清华大学出版社)第32–35页]
[11] Badii R, Broggi G, Derighetti B, Ravani M 1988 Phys. Rev. Lett. 60 979
[12] Tung W W, Gao J B, Hu J, Yang L 2011 Phys. Rev. E 83 046210
[13] Gao J B, Sultan H, Hu J, Tung W W 2010 IEEE Signal Proc. Lett. 17 237
[14] Donoho D L 1995 IEEE Trans. Inform. Theory 41 613
[15] Han M, Liu Y H, Xi J H, Guo W 2007 IEEE Signal Proc. Lett. 14 62
[16] Cawley R, Hsu G H 1992 Phys. Rev. A 46 3057
[17] Schreiber T, Richter M 1999 Int. J. Bifurcation Chaos 9 2039
[18] Kopsinis Y, McLaughlin S 2009 IEEE Trans. Signal Proc. 57 1351
[19] Wang W B, Zhang X D, Wang X L 2013 Acta Phys. Sin. 62 050201 (in Chinese) [王文波, 张晓东, 汪祥莉 2013 62 050201]
[20] Feng J C 2005 Chin. Phys. Lett. 22 1851
[21] Arasaratnam I, Haykin S, Hurd T R 2010 IEEE Trans. Signal Proc. 58 4977
[22] Curtis F, Patrick O (translated by L S J) 2006 Applied Numerical Analysis (Beijing: China Machine Press) pp164-166 (in Chinese) [柯蒂斯F, 帕特里克O 著(吕淑娟 译) 2006 应用数值分析(北京: 机械工业出版社)第164–166页]
[23] Schafer R W 2011 IEEE Signal Proc. Mag. 28 111
[24] Savitzky A, Golay M J E 1964 Anal. Chem. 36 1627
[25] Krishnan S R, Seelamantula C S 2013 IEEE Trans. Signal Proc. 61 380
[26] Vivó-Truyols G, Schoenmakers P J 2006 Anal. Chem. 78 4598
[27] Chen G R, Ueta T 1999 Int. J. Bifurcation Chaos 9 1465
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