中文摘要：

对信号和噪声在小波域的性态分析对于噪声的滤除具有重要的意义。推导出信号的样条二进小波变换系数幅值沿尺度的变化趋势依赖于信号的奇数阶导数,高斯白噪声的样条二进小波变换系数方差沿尺度逐渐衰减且衰减率越来越小。提出了一种基于小波域性态分析的组合滤波方法,仿真实验表明了算法的有效性。

英文摘要：

Analyzing property of signal and noise in wavelet domain is of great importance for noise reduction. It was proved that the amplitude of spline dyadic wavelet transform of signal depended on its odd order derivation, while variance of wavelet transform coefficients of white Gaussian noise decreased at a decreasing rate across scales. Therefore, a combination filtering based on analysis of property in wavelet domain was proposed Simulations verify the effectiveness of the algorithm.