li5-39

循环平稳信号是一类特殊的非平稳信号，其统计特征具有随时间呈周期变化的特点。旋转机械由于周期运行方式其振动信号具有循环平稳特性，因此利用循环平稳分析方法能够提取出在平稳假设下所不能得到的隐藏故障特征信息，为有效地分离和识别旋转机械早期微弱故障特征提供可能。(The cyclostationary signal is a special type of non-stationary signal whose statistical characteristics have a periodic variation with time. Due to the cyclical operation of the rotating machinery, the vibration signal has the characteristics of cyclostationary stability. Therefore, the cyclostationary analysis method can extract the hidden fault feature information that can not be obtained under the stationary assumption, which provides the possibility to effectively separate and identify the early weak fault features of the rotating machinery.)

实现小波变换，小波滤波器，小波除噪等功能。(To achieve wavelet transform, wavelet filters, wavelet denoising function)

说明：  用c++实现小波变换，参考matlab实现(Using C + + to realize wavelet transform, referring to matlab to realize)

说明：  带有多种小波基的小波变换程序，可用于图象识别，信号突变检测。(with multiple small Porgy wavelet transform procedures can be used to image recognition, signal mutation detection.)

在实数域 ,对称、 正交的紧支集非平凡单小波基不存在 ,而多小波把紧支集，对称性、 正交性完美地结合在一起 ,使小波理论从标量扩展到矢量范畴。利用上述特点将多小波变换应用于 SAR 图像压缩。(In the real fields, symmetric, orthogonal set of nontrivial compactly supported wavelet basis does not exist alone, but more than the compact support wavelet, symmetry, orthogonality perfect combination, So wavelets theory extended Dao vector from scalar context. Use of these features will be more than SAR image compression wavelet transform.)

a matlab code for applying wavelet decomposition usuful for compression schema

matlab计算haar 小波各级近似系数和细节系数的频率响应（CA1，CD1，CA2，CD2，CA3），并画出幅频图，便于理解小波变换的意义，(U191 u7197 u5c1 u5c1 u5Fc1 u4Fc u653 u564C u548C u7286 u8282 u7CFB u6570 u7684 u9891 u54CD u5E94 uFF08CA1 uFF0CCD1 uFF0CCA2 uFF0CCD2 UFF0CCA3 uFF09 uFF0C u5E76 u753B u51FA u5E45 u9891 u56FE uFF0C u4FBF u4E8E u7406 u89E3 u5C0F u6CE2 u53D8 u6362 u7684 u610F u4E49 uFF0C)

图象增强小波变换将一幅图象分解为大小、位置与方向都不同的分量。在做逆变换之前能改变小波变换域中某些系数的大小，，这样就能够洋选择的放大所感兴趣的分量而减小不需要的分量。给定一个图象信号，用二维小波分析析对图象进行增强处理。 (Image enhancement wavelet transform decomposition size, location and direction of the different components of an image. Wavelet transform domain, some the size of the coefficient can change before doing the inverse transformation, so can the component of interest to the amplification of the ocean choose to reduce the unwanted weight. Given an image signal, the analysis of two-dimensional wavelet analysis of image enhancement processing.)

某一直升机齿轮箱上的早期损伤的特征是，在伴随振动信号上产生一个可变周期的非平稳扰动信号。要求按此特征构造一组有物理意义的数据仿真早期故障信号，应用小波变换技术分析故障的特征和发生时刻。(a helicopter gearbox early on the characteristics of the injury, In addition to the vibration signal produced a variable cycle perturbation of non-stationary signals. Click here to request a group of tectonic significance of a physical early fault simulation data signals Application of wavelet transform technical analysis of the features and fault occurred moments.)

小波变换阈值去噪的文章，基于最大最小准则计算(Minimax Estimation, Adaptive Estimation, Nonparametric Regression, Density Estimation, Spatial Adaptation, Wavelet Orthonormal bases, BesovSpaces, Optimal Recovery.)