非平稳信号分解的多元快速迭代滤波
Multivariate Fast Iterative Filtering for the decomposition of nonstationary signals
摘要：
在这项工作中，我们提出了一种新的技术，我们称之为多元快速迭代滤波（MvFIF）算法的多变量数据的分解。我们研究了它的性质，严格证明了它适用于任何类型的多元信号的分解时，在有限时间内收敛。我们测试MvFIF性能使用各种各样的人工和真正的多元信号，显示其能力：分离多元调制振荡;对齐频率沿不同的通道;产生一个准-二进滤波器组时，分解白高斯噪声;分解信号中的一个准-正交组的组件;是强大的噪声扰动，即使当通道的数量大大增加。最后，我们将其性能与文献中迄今为止开发的主要方法之一进行比较，证明MvFIF在没有任何先验假设的情况下，以快速可靠的方式对所研究的信号进行唯一定义的任何多变量信号的分解。
英文摘要：
In this work, we present a new technique for the decomposition of multivariate data, which we call Multivariate Fast Iterative Filtering (MvFIF) algorithm. We study its properties, proving rigorously that it converges in finite time when applied to the decomposition of any kind of multivariate signal. We test MvFIF performance using a wide variety of artificial and real multivariate signals, showing its ability to: separate multivariate modulated oscillations; align frequencies along different channels; produce a quasi--dyadic filterbank when decomposing white Gaussian noise; decompose the signal in a quasi--orthogonal set of components; being robust to noise perturbation, even when the number of channels is increased considerably. Finally, we compare its performance with the one of the main methods developed so far in the literature, proving that MvFIF produces, without any a priori assumption on the signal under investigation and in a fast and reliable manner, a uniquely defined decomposition of any multivariate signal.
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