中文摘要：

为降低混沌信号中常见的白噪声及脉冲噪声,提出了改进的小波阈值降噪与S-G（Savitzky-Golay）滤波相结合的方法。小波基函数和分解层数对降噪效果有着重要影响,为取得更好的降噪效果,采用逐层确定最优基小波和分解层数自适应确定方法,并给出了各层阈值的选取方法,最后将改进的加权法应用于S-G小波去噪方法以恢复高频分量中部分有用信号。利用该方法对Lorenz混沌时间序列及实测机械式混沌振动信号进行了去噪研究,结果表明所提方法能将混沌信号信噪比提高近1 d B,自相关函数值提高0.01,是一种有效的混沌信号降噪新方法。

英文摘要：

In this paper,we present a hybrid method based on improved wavelet threshold denoising and the Savitzky-Golay（ S-G） filter to reduce the commonly seen white and pulse noises in chaotic signals. The wavelet-based function and the number of decomposed levels have a significant influence on the noise reduction effect,and in order to improve this noise reduction effect,we confirm the optimal basis wavelet level by level and the number of decomposed levels by adaptivity. A method for selecting the threshold value at each level is also given. Finally,we applied the improved weighting method to the S-G and wavelet denoising method to restore some useful signals in the high frequency component. We used the proposed denoising method to investigate the denoising of a Lorenz chaotic time series and measured the mechanical chaotic vibration signal. The results show that the proposed method enhanced the signal-to-noise ratio（ SNR） by 1 d B and the autocorrelation function value by 0.01. Based on our results,we conclude that the proposed method is an effective chaotic signal denoising method.