Iterative Filtering (IF) is an alternative technique to the Empirical ModeDecomposition (EMD) algorithm for the decomposition of non-stationary andnon-linear signals. Recently in [1] IF has been proved to be convergent for any$L^2$ signal and its stability has been also showed through examples.Furthermore in [1] the so called Fokker-Planck (FP) filters have beenintroduced. They are smooth at every point and have compact supports. Based onthose results, in this paper we introduce the Multidimensional IterativeFiltering (MIF) technique for the decomposition and time-frequency analysis ofnon-stationary high-dimensional signals. And we present the extension of FPfilters to higher dimensions. We illustrate the promising performance of MIFalgorithm, equipped with high-dimensional FP filters, when applied to thedecomposition of 2D signals. [1] A. Cicone, J. Liu, and H. Zhou, Adaptive local iterative filtering forsignal decomposition and instantaneous frequency analysis, arXiv:1411.6051,2014.
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机译：迭代滤波（IF）是经验模态分解（EMD）算法的一种替代技术，用于分解非平稳和非线性信号。最近，在[1]中，IF被证明对任何L ^ 2 $信号都是收敛的，并且还通过示例证明了它的稳定性。此外，在[1]中，引入了所谓的Fokker-Planck（FP）滤波器。它们的每一点都很光滑，并具有紧凑的支撑。基于这些结果，本文介绍了多维迭代滤波（MIF）技术，用于非平稳高维信号的分解和时频分析。而且，我们提出了将FPfilters扩展到更高维度的方法。当说明将MIF算法应用于2D信号分解时，我们将展示它的前景。 [1] A. Cicone，J。Liu和H. Zhou，信号分解和瞬时频率分析的自适应局部迭代滤波，arXiv：1411.6051，2014。
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