The development of methods able to extract hidden features from non-stationary and non-linear signals in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem of further analyzing the convergence of the Iterative Filtering method both in a continuous and a discrete setting in order to provide a comprehensive analysis of its behavior. Based on these results we provide a new efficient implementation of Iterative Filtering algorithm, called Fast Iterative Filtering, which reduces the original iterative algorithm computational complexity by utilizing, in a nontrivial way, Fast Fourier Transform in the computations.

中文翻译：

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基于 FFT 的新型高效实现迭代滤波的数值分析

开发能够以快速可靠的方式从非平稳和非线性信号中提取隐藏特征的方法在许多研究领域都具有重要意义。在这项工作中，我们解决了进一步分析迭代过滤方法在连续和离散设置中的收敛性的问题，以便对其行为进行全面分析。基于这些结果，我们提供了一种新的迭代滤波算法的有效实现，称为快速迭代滤波，它通过在计算中以一种非平凡的方式利用快速傅立叶变换来降低原始迭代算法的计算复杂度。