EMD算法分解信号后，怎么将这些信号重构呢求高手指点

有个叫BOUDRAA的人发明了一种算法，叫连贯均方误差法，就是分别求每个IMF分量的平方，取完后求和再取平均，求和的点数是N，即采样点的点数。假如你分解得到了M个IMF分量，那么就应该有M个这样的数，把得到的这些数圆整，求出最小的整数，记为K。那么K之前的包括K的这些分量相加应该是噪声的信号，K之后的加上剩余信号即为重构信号。不过目前该方法被证实不适合信噪比低得信号，不过一般的处理效果还可以。

号的方法，从根本上有

别于传统的信号时频分析方法，并在实际应用中取得了很好的效果。

EMD分解算法通过层层筛选，得到信号不同时间特征尺度的IMF分量。EMD

分解的主要目的是为了将信号进行平稳化处理，对IMF分量进行Hilbert变换，进

一步得到IMF分量对应的瞬时频率成分，这样得到的瞬时频率有了合理的物理意

义。通过Hilbert得到的的Hilbert/Huang频谱图是时间和频率的二变量函数，从中

可以得到任意时刻的频率信息，包括频率的大小和幅度以及出现的对应时刻，能

够详细的刻画非平稳非线性信号的时频特性。

emd是经验模态分解。

经验模态分解（Empirical Mode Decomposition，简称EMD）是依据数据自身的时间尺度特征来进行信号分解，无须预先设定任何基函数。

这一点与建立在先验性的谐波基函数和小波基函数上的傅里叶分解与小波分解方法具有本质性的差别。

正是由于这样的特点，EMD方法在理论上可以应用于任何类型的信号的分解，因而在处理非平稳及非线性数据上，具有非常明显的优势，适合于分析非线性、非平稳信号序列，具有很高的信噪比。

经验模态分解的原理：

经验模态分解(EMD)方法的实质是通过特征时间尺度来识别信号中所内含的所有振动模态(Intrinsic Oscillatory Mode)。

在这一过程中，特征时间尺度及IMF的定义都具有一定的经验性和近似性。与其他信号处理方法相比，EMD方法是直观的、间接的、后验的、自适应的，其分解所用的特征时间尺度是源自于原始信号的。

1 introduction

Empirical Mode Decomposition Empirical Mode Decomposition (EMD) is the midlands, in 1998, a new kind of signal processing method In 1999, the midlands and some improvements were made to it This method is introduced from the signal processing field, it's got the corresponding improvement How to use the program developed by EMD theory as the core of the nonlinear unstable signal processing system, realize the potential value theory of EMD, and the economic value is the focus of current signal field

MATLAB is a highly integrated, set scientific computing, program design and visualization in software environment In this software, problems and physical appearances in problem of familiar, its mathematical form typical applications include: mathematics and computation, Algorithm, Modeling and simulation, Numerical analysis, testing and visualization, Application development (including a graphical user interface), etc

This paper firstly introduces the main ideas; EMD Then give the method of "screen" contained in the process of solving problems and solutions for these problems to solve the effective realization of EMD laid a foundation, Finally the nonlinear unstable signal processing system and the flowchart of signal and system function of graphical interface, generating method, and the computation module function and structure, thus realizing the EMD method on the basis of EMD method as the core, with GUI interface, as a system of practical value nonlinear unstable signal processing system

2 empirical mode decomposition method

Empirical mode decomposition method is essentially a signal (or its derivative, depending on the accuracy of the required) smoothly, the result will be different scales of signal wave or trend level, a series of decomposition with different characteristics of the scale, each sequence data sequence is called a the eigenmode Function (IntrinsicMode hire those knowledgeable programmers, the IMF) The lowest frequency components of the IMF usually represent the original signal trend or value As an application, EMD method can effectively extract a data sequences or remove the trend of average data sequences Test results show that the method is currently extract data EMD trend or sequence of mean best method, the method of another EMD aims to further to the IMF Hilbert transformation, simultaneously the signal feature The instantaneous

3 EMD method two difficult problem

EMD method is the key step of the process, "screen" by over the original signal, the screen each IMF component and trends Through each IMF component of Hilbert transformation, to get the weight of the instantaneous characteristics corresponding, complex signal feature extraction "The screening process of" two problems: met (1) how to get the maximum signal, especially the tip of extreme value point; (2) does not contain complex signal processing, the IMF only contains original signal trend of judgment Only in the above two problems solved properly, and on the basis of EMD method and signal processing system

Be true

4 the nonlinear unstable signal processing system

The nonlinear unstable signal processing system is based on the increase, EMD GUI interface as system Graphical interface, man-machine interface is responsible for completing the signal EMD method This section of this system are presented first signal processing flow chart, then respectively expounds system interface method of generating and function, and the functional and structural computation modules

5 conclusion

This paper introduces the empirical mode decomposition method, it can be for nonlinear unstable signals obtained several hierarchically, IMF component, through each component of the transient feature extraction, complete complex signal feature extraction Then solve the EMD method "screening process of" two important issues: the endpoint and decompose the IMF component loop ends when conditions To solve the problems of endpoint for empirical mode decomposition method, the nonlinear unstable signal processing system laid a theoretical foundation Finally, the paper puts forward the system processing flow chart and system interface signal generation methods of function and the computation module, two big functions and structure In empirical mode decomposition method, on the basis of graphical interface encapsulation realized by nonlinear unstable signal processing system This system not only realized the EMD method of generating the theoretical value, but realized what it contains the practical value

这个分解是基于希尔伯特-黄变换和希尔伯特变换而来，通过黄变换滤除信号里局域的直流成分，短时内是纯交流成分。而之所以不直接使用希尔伯特变换后利用复信号的d(phi)/dt=w (phi是角度）的方式来求信号的瞬时频率，是因为信号可能存在非频率波动的成分，也就是说可能信号的波动是因幅值引起，这样求得的频率可能是负值，而希尔伯特变换的信号频率不存在负的，所以才需要以上的黄变换这个分解imf的过程。但这个分解精度纯粹因信号本身而异，存在一定的风险。不过据我认为，信号在离散的情况下，黄变换并不是必须的，只需要在希尔伯特变换之前加一些简单处理即可，这种方式得到的瞬时频率与用了imf后得到的再matlab下得到的图像基本一样。楼主可自己编写程序，这个程序包不是必须

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