标题： 一种用于分解非平稳多维和多变量信号的新算法 显示英文标题

标题： A novel algorithm for the decomposition of non-stationary multidimensional and multivariate signals

摘要： 信号的分解是许多研究领域中的基本工具，包括信号处理、地球物理学、天体物理学、工程学、医学等等。 通过将复杂的信号分解为更简单的振荡成分，我们可以增强对数据的理解和处理，揭示其中隐藏的信息。 传统的分析方法，如傅里叶分析和小波变换，在处理一维平稳信号时是有效的，但它们难以应对非平稳的数据集，并且需要预先选择基函数（例如小波的情况）。 相比之下，经验模式分解（EMD）方法及其变种，如迭代滤波（IF），作为有效的非线性方法出现，能够适应信号而无需任何先验假设。 为了加速这些方法，开发了快速迭代滤波（FIF）算法，并提出了进一步的扩展，如多变量FIF（MvFIF）和多维FIF（FIF2），以处理更高维度的数据。 在这项工作中，我们介绍了多维多变量快速迭代滤波（MdMvFIF）技术，这是一种创新的方法，将FIF扩展到处理同时在空间和时间上变化的数据。 这一新算法能够从同时在空间和时间上变化的复杂信号中提取固有模式函数（IMFs），克服了先前方法中存在的限制。 该方法的潜力通过应用于人工信号和真实生活信号的实例得到了证明，突显了其在分解多维和多变量非平稳信号方面的多功能性和有效性。 MdMvFIF方法为科学和工程学科中的高级信号分析提供了一个强大的工具。 显示英文摘要

摘要： The decomposition of a signal is a fundamental tool in many fields of research, including signal processing, geophysics, astrophysics, engineering, medicine, and many more. By breaking down complex signals into simpler oscillatory components we can enhance the understanding and processing of the data, unveiling hidden information contained in them. Traditional methods, such as Fourier analysis and wavelet transforms, which are effective in handling mono-dimensional stationary signals struggle with non-stationary data sets and they require, this is the case of the wavelet, the selection of predefined basis functions. In contrast, the Empirical Mode Decomposition (EMD) method and its variants, such as Iterative Filtering (IF), have emerged as effective nonlinear approaches, adapting to signals without any need for a priori assumptions. To accelerate these methods, the Fast Iterative Filtering (FIF) algorithm was developed, and further extensions, such as Multivariate FIF (MvFIF) and Multidimensional FIF (FIF2), have been proposed to handle higher-dimensional data. In this work, we introduce the Multidimensional and Multivariate Fast Iterative Filtering (MdMvFIF) technique, an innovative method that extends FIF to handle data that vary simultaneously in space and time. This new algorithm is capable of extracting Intrinsic Mode Functions (IMFs) from complex signals that vary in both space and time, overcoming limitations found in prior methods. The potentiality of the proposed method is demonstrated through applications to artificial and real-life signals, highlighting its versatility and effectiveness in decomposing multidimensional and multivariate nonstationary signals. The MdMvFIF method offers a powerful tool for advanced signal analysis across many scientific and engineering disciplines.