基于混沌理论和小波变换的微弱周期信号检测方法

根据小波变换具有多分辨率,混沌系统对噪声的强免疫力和对周期微弱信号的敏感性等特性,通过对小波阈值去噪方法和混沌Duffing振子方程的改进,提出小波阈值去噪和混沌系统相结合的微弱周期信号检测新方法.该方法利用小波变换的平滑作用对包含噪声的信号进行有限离散处理,并根据小波分解尺度确定阈值去噪深度,然后把重构的信号作为周期策动力的摄动并入混沌系统,采用混沌振子阵列实现在噪声背景下微弱信号的检测,并采用梅尔尼科夫方法作为混沌判据.该检测方法克服了以往小波分解对尺度确定的盲目性和阈值选择的不合理性以及对混沌临界状态与周期态区别的模糊性:同时能检测多种频率的信号.仿真测试表明:该方法直观、高效,检测精度高,检测的最低信噪比达到-100dB,频率误差为0.04％左右,改善了湮没在强噪声下的微弱信号检测技术.

Weak periodical signal detection based on wavelet threshold de-noising and chaos theory

Based on the multi-resolution of wavelet transform and chaotic system having a good immunity to noise and sensitive to weak periodical signal,a new method of weak signal detection was proposed based on the combination of the wavelet threshold de-noising and chaotic system by improving wavelet threshold de-noising and duffing oscillator.This method uses wavelet smoothing effect to the limited discrete processing of the signal that contains noise and uses the scale of the wavelet decomposition to determine the de-nosing depth,and then uses the reconstructed signal as the driving motivation of the perturbation cycle into the chaotic system.The chaotic oscillator array is applied to detect weak signal in noisy background,and Melnikov method is adopted as chaotic criterion.This new method has overcome the blindness to the determination of scale and irrationality choice to the threshold of past method of the wavelet decomposition,as well as the ambiguity to distinguish between the critical state and periodic motion state.At the same time,multi-frequency signal can be detected.The simulation results indicate that this detection method is simple and effective,and the detection precision is high.The minimum detection SNR reaches -100 dB and the frequency error is about 0.04%.The weak signal buried in strong noise detection method is improved.