Extractraction of non-stationary harmonic from chaotic background based on synchrosqueezed wavelet transform

The signal detection in chaotic background has gradually become one of the research focuses in recent years. Previous research showed that the measured signals were often unavoidable to be contaminated by the chaotic noise, such as the radar signal detection from sea clutter wave,signal source extraction from chaotic secure communication and ECG/EEG abnormal signal detection,etc.At present,there are two methods to detect the target signal from the chaotic background.One is to detect the target signals by using the difference in geometric structure between the chaotic signal and the target signal,and the other is to regard the chaotic signal as the noise,and the target signal is extracted from the chaotic background by the time frequency analysis method,such as wavelet transform and empirical mode decomposition. The first kind of method can detect the target signal well,but it needs to characterize the chaotic system and reconstruct the phase space,which is difficult in the practical applications.The second kind of method does not need to reconstruct the chaotic phase space and can effectively extract the target signal from the chaotic background.However,the wavelet transform lacks adaption and how to select the optimal wavelet basis and decomposition layers is a difficult problem.In the empirical mode decomposition there exists the mode mixing that is very sensitive to the noise.The synchrosqueezed wavelet transform (SST) effectively improves the mixing of mode by compressing the continuous wavelet coefficients in the frequency direction,but also it has good robustness to noise.Therefore,the SST can extract the harmonic signal well from the chaotic background.In the present algorithm of abstracting harmonic signal from chaotic background by SST,the harmonic signals are extracted by using single accumulation frequency range SST (SAFR-SST) based on wavelet ridge detection.If the target signal is stable harmonic signal,whose frequency does not change with time,the SAFR-SST method can have a high abstraction precision.But if the target signal is the non-stable harmonic signal whose frequency changes with time,the SAFR-SST method is not enough nor can obtain high abstraction precision.In order to overcome the shortcomings of the SST in extracting the non-stationary harmonic signal from the chaotic background, an improved SST extracting method is proposed which is based on the adaptive optimal cumulative frequency range. Firstly,the formulas of calculating the adaptive cumulative frequency range in SST extraction are deduced according to the relationship between the wavelet coefficient of non-stationary harmonic and the interval of supporting wavelet bases.Then,the optimal values of the parameters in the adaptive cumulative frequency range formula are calculated by the minimum energy error criterion according to the integrity and orthogonality of the intrinsic mode types function.Finally,the SST adaptive extraction of the non-stationary harmonic signal is realized according to the SST inverse transform.In experiment,the different types of non-stationary harmonics are extracted from the Lorenz and Duffing chaotic background.The experimental results show that the proposed method can effectively extract the non-stationary harmonic from the noisy chaotic background.Compared with the classical SST method with single cumulative frequency range,the proposed method has good performance in both mean square error and correlation coefficient.And when the chaotic background contains different-intenity Gauss white noises,the proposed method can also effectively abstract the non-stationary harmonic from the chaos and noise interference.So,the proposed method has a good practice value.