基于高阶阈值函数与小波包的混沌信号降噪

Noise reduction of chaotic signals based on high-order threshold function and wavelet packet

针对混沌信号小波降噪法中,高频段频率分辨率较差,且对小波分解系数所广泛采用的硬、软阈值量化方法存在着局限等问题,给出一种基于新型高阶阈值函数的混沌信号小波包降噪法.该方法采用小波包方法能够对小波分析中没有细分的高频部分进一步分解,保留了有用的高频信息,从而具有更加精确的局部分析能力;且所采用的阈值函数连续光滑,在噪声小波系数和混沌信号小波系数之间存在一个平滑过渡区,更符合信号的连续特性.仿真对比实验表明：与软阈值降噪法以及半软阈值与小波包降噪法相比,该方法对混沌信号的降噪效果明显,信噪比（SNR）有3.7 ～7 dB的显著提高.

The conventional threshold function in wavelet noise reduction of chaotic signals has its shortages,such as low resolution of high frequency and restraint limit of quantitative method to hard and soft thresholds.Concerning these shortages,a wavelet packet noise reduction method of chaotic signals was proposed based on a high-order threshold function.The method could further decompose high frequency part by wavelet packet and retained useful high-frequency information,so it was more precious in partial analysis.Furthermore the threshold function was continuous and derivable.There was a smooth transiting area between noise wavelet coefficient and chaotic signal wavelet coefficient.As a result,it is more consistent with the continuous characteristics of the signal.The comparative simulation shows that,compared with soft threshold noise reduction method and semi-soft threshold wavelet packet noise reduction method,the effect of noise reduction to chaotic signals has been significantly improved,and Signal-to-Noise Ratio （SNR） increased 3.7-7 dB.