Parseval Theory of Complex Wavelet Transform for Wavelet Family Including Rotational Parameters

A rotational parameter R_θ has been introduced to complex wavelet transform (CWT).The rotational CWT(RCWT) corresponds to a matrix element 〈ψ|U_2(θ;μ;k)|F〉 in the context of quantum mechanics,where U_2(θ;μ;k) is atwo-mode rotational displacing-squeezing operator in the 〈η| representation.Based on this,the Parseval theorem andthe inversion formula of RCWT have been proved.The concise proof not only manifestly shows the merit of Dirac'srepresentation theory but also leads to a new orthogonal property of complex mother wavelets in parameter space.

基于量子高斯混合模型的振动信号降噪方法

由于机械设备振动信号受到背景噪声的干扰,造成机械设备故障状态特征不明显,因此提出了一种基于量子高斯混合模型的振动信号降噪方法。首先,对振动信号进行双树复小波包变换,对双树复小波包系数建立高斯混合模型,根据贝叶斯最大后验估计准则,得到双树复小波包系数收缩函数;然后,利用双树复小波包系数父代和子代的空间相关性,结合量子叠加态理论计算噪声信号和有用信号小波系数出现的概率值;最后,根据量子叠加态得到的概率参数值调节高斯混合模型中的小波包系数收缩函数,使小波包系数自适应非线性收缩,提高高斯混合模型的局部自适应性,实现机械振动信号的降噪处理。仿真信号和实测行星齿轮箱振动信号实验结果表明,该方法能够有效地去除振动信号中的噪声,凸显机械设备的故障状态特征。