matlab信号处理emd工具箱

上传者: 41794955 | 上传时间: 2023-02-22 15:18:20 | 文件大小: 2.94MB | 文件类型: ZIP
经验模态分解(Empirical Mode Decomposition,EMD)法是黄锷(N. E. Huang)在美国国家宇航局与其他人于1998年创造性地提出的一种新型自适应信号时频处理方法,特别适用于非线性非平稳信号的分析处理。对经过EMD处理的信号再进行希尔伯特变换,就组成了大名鼎鼎的“希尔伯特—黄变换”(HHT)。由于脑电信号处理很少在EMD之后接上希尔伯特变换,在这里仅介绍EMD的相关基础知识。   EMD其实就是一种对信号进行分解的方法,与傅里叶变换、小波变换的核心思想一致,大家都想将信号分解为各个相互独立的成分的叠加;只不过傅里叶变换以及小波变换都要求要有基函数,而EMD却完全抛开了基函数的束缚,仅仅依据数据自身的时间尺度特征来进行信号分解,具备自适应性。由于无需基函数,EMD几乎可以用于任何类型信号的分解,尤其是在非线性、非平稳信号的分解上具有明显的优势。   EMD的目的是将信号分解为多个本征模函数(IMF)的叠加。IMF必需要满足以下两个条件:   (1)函数在整个时间范围内,局部极值点和过零点的数目必须相等,或最多相差一个;   (2)在任意时刻点,局部最大值的包络(上包络线)和局部最小值的包络(下包络线) 平均必须为零。   为什么IMF一定要满足这两个条件呢?经黄锷等人的研究,满足这两个条件的信号都是单组分的,相当于序列的每一个点只有一个瞬时频率,无其他频率组分叠加。这就为后续的希尔伯特变换铺平了道路,也使得瞬时频率有了意义。   值得一提的是,EMD在数学上还有一些细节无法证明,但是EMD已经在工程领域取得了辉煌的成就,这也是在科学界工程领先理论的一个例子。

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