基于双提升小波的自适应混沌信号降噪

摘要

根据信号和噪声的特性不同,本文提出了一种基于双提升小波的自适应混沌信号降噪方法.该方法结合奇异谱和梯度下降算法,分别对双提升小波变换后的近似部分和细节部分进行了分析.一方面,奇异谱分析更大程度的去除了代表噪声的较小奇异值;另一方面,神经网络对非线性阈值的自学习,实现了小波系数的自适应选取,提高了信号的定位精度.通过对Lorenz模型和月太阳黑子时序进行仿真,证实了本文所提方法能够对实际观测的混沌信号进行有效的降噪.%According to different characteristics of chaotic signals and Gaussian noises, an adaptive noise reduction method is proposed based on dual-lifting wavelet. Singular spectrum analysis (SSA) and gradient decent algorithm are respectively used for the analysis of coarse approximation and detail information. The former removes smaller singular value representing noises in a greater degree, while the latter employed for the adaptive choice of wavelet coefficients further improves the positioning accuracy of signals. The chaotic signals generated by Lorenz model as well as the observed monthly series of sunspots are applied for simulation analysis, the numerical experiment results confirm that the adaptive method in this paper is effective for noise reduction of chaotic signals.