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Extracting the harmonic signal from the chaotic interference background is very important for theory and practical application. The wavelet transform and empirical mode decomposition (EMD) have been widely applied to harmonic extraction from chaotic interference, but because the wavelet and EMD both present the mode mixing and are sensitive to noise, the harmonic signal often cannot be precisely separated out. The synchrosqueezing wavelet transform (SST) is based on the continuous wavelet transform, through compressing the time-frequency map of wavelet transform in the frequency domain, the highly accurate time-frequency curve is obtained. The time-frequency curve of SST which does not exist between cross terms, can better improve the mode mixing. The SST has also good robustness against noise. When the signal is a mixed strong noise, the SST can still obtain the clear time-frequency curve and approximate invariant decomposition results. In this paper, the SST is applied to the multiple harmonic signal extraction from chaotic interference background, and a new harmonic extracting method is proposed based on the SST. First, the signal obtained by mixing chaotic and harmonic signals is decomposed into intrinsic mode type function (IMTF) by the SST. Then using the Hilbert transform the frequency of each IMTF is analyzed, and the harmonic signals are separated from the mixed signal. Selecting the Duffing signal as the chaotic interference signal, the extracting ability of the proposed method for multiple harmonic signals is analyzed. The different harmonic extraction experiments are conducted by using the proposed SST method for different frequency intervals and different noise intensity multiple harmonic signals. And the experimental results are compared with those from the classical EMD method. When the chaotic interference signal is not contained by noise, the harmonic signal extraction effect is seriously affected by the frequency interval between harmonic signals. If the harmonic frequency interval between harmonic signals is relatively narrow, each harmonic signal cannot be accurately extracted by the EMD method. However, the harmonic extraction precision of SST method is not seriously influenced by the change of harmonic frequency interval, and when the frequency interval between harmonic signals is small the SST method can still accurately extract each harmonic signal from chaotic interference. When the noise contains a chaotic interference signal, the harmonic extraction effect of EMD method significantly decreases with noise intensity increasing. When the noise level reaches 80%, the extracted harmonic signal from the EMD method is seriously distorted, the correlation coefficient of the extracted harmonic signal with original harmonic signal is only about 0.6. With the increase of noise intensity, the harmonic extraction effect of SST method has also a declining trend. But as the noise intensity is within 120%, the harmonic extraction effect of SST method does not greatly change and the extracted harmonic signal precision is still higher, which shows that the harmonic extraction method based on the SST has good robustness against noise. The comprehensive experimental results show that the proposed SST method has high extracting precision for multiple harmonic signals of different frequency intervals, and the SST method has better robustness against Gauss white noise. The extracted results of harmonic signal are better than those from the classical empirical mode decomposition method.
[1] Wang W B, Zhang X D, Wang X L 2013 Acta Phys. Sin. 62 069701 (in Chinese) [王文波, 张晓东, 汪祥莉 2013 物理学报 62 069701]
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[16] Liu J L, Ren W X, Wang Z C, Hu Y D 2013 J. Vib. Shock 32 37 (in Chinese) [刘景良, 任伟新, 王佐材, 胡异丁 2013 振动与冲击 32 37]
[17] Daubechies I, Lu J F, Wu H T 2011 Appl. Computat. Harmon. Anal. 2 243
[18] Wu H T 2013 Appl. Computat. Harmon. Anal. 35 181
[19] Gaurav T, Eugene B, Neven S F, Wu H T 2012 Sign. Process. 93 1079
[20] Sylvain M, Thomas O, Stephen M 2012 IEEE Trans. Sign. Process. 60 5787
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[1] Wang W B, Zhang X D, Wang X L 2013 Acta Phys. Sin. 62 069701 (in Chinese) [王文波, 张晓东, 汪祥莉 2013 物理学报 62 069701]
[2] Lu K, Wang F Z, Zhang G L, Fu W H 2013 Chin. Phys. B 22 120202
[3] Li T Z, Wang Y, Luo M K 2013 Chin. Phys. B 22 080501
[4] Lu S X, Wang Z S, Hu Z H, Feng J C 2014 Chin. Phys. B 23 010506
[5] Xing H Y, Cheng Y Y, Xu W 2012 Acta Phys. Sin. 61 100506 (in Chinese) [行鸿彦, 程艳燕, 徐伟 2012 物理学报 61 100506]
[6] Leung H, Huang X P 1996 IEEE Trans. Sign. Process. 44 2456
[7] Haykin S, Li X B 1995 Proc. IEEE 83 94
[8] Stark J, Arumugaw B 1992 Int. J. Bifurc. Chaos 2 413
[9] Wang F P, Guo J B, Wang Z J 2001 Acta Phys. Sin. 50 1019 (in Chinese) [汪芙平, 郭静波, 王赞基 2001 物理学报 50 1019]
[10] Huang N E, Shen Z, Long S R 1998 Proc. Roy. Soc. London A 454 903
[11] Wang G G, Wang S X 2006 J. Jilin Univ. (Sci. Ed.) 44 439 (in Chinese) [王国光, 王树勋 2006 吉林大学学报（理学版） 44 439]
[12] Li H G, Meng G 2004 Acta Phys. Sin. 53 2069 (in Chinese) [李鸿光, 孟光 2004 物理学报 53 2069]
[13] Wang E F, Wang D Q, Ding Q 2011 J. Commun. 32 60 (in Chinese) [王尔馥, 王冬青, 丁群 2011 通信学报 32 60]
[14] Wang E F, Wang D Q 2012 J. Engineer. Heilongjiang Univ. 3 105 (in Chinese) [王尔馥, 王冬青 2012 黑龙江大学工程学报 3 105]
[15] Chen G D, Wang Z C 2012 Mech. Syst. Sign. Process. 28 259
[16] Liu J L, Ren W X, Wang Z C, Hu Y D 2013 J. Vib. Shock 32 37 (in Chinese) [刘景良, 任伟新, 王佐材, 胡异丁 2013 振动与冲击 32 37]
[17] Daubechies I, Lu J F, Wu H T 2011 Appl. Computat. Harmon. Anal. 2 243
[18] Wu H T 2013 Appl. Computat. Harmon. Anal. 35 181
[19] Gaurav T, Eugene B, Neven S F, Wu H T 2012 Sign. Process. 93 1079
[20] Sylvain M, Thomas O, Stephen M 2012 IEEE Trans. Sign. Process. 60 5787
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