Many real-life signals are defined on spherical domains, in particular in geophysics and physics applications. In this work, we tackle the problem of extending the iterative filtering algorithm, developed for the decomposition of non-stationary signals defined in Euclidean spaces, to spherical domains. We review the properties of the classical Iterative Filtering method, present its extension, and study its convergence in the discrete setting. In particular, by leveraging the Generalized Locally Toeplitz sequence theory, we are able to characterize spectrally the operators associated with the spherical extension of Iterative Filtering, and we show a counterexample of its convergence. Finally, we propose a convergent version, called Spherical Iterative Filtering, and present numerical results of its application to spherical data.

翻译：许多实际信号定义在球面域上，尤其是在地球物理学和物理学应用中。本研究针对如何将针对欧几里得空间中非平稳信号分解而发展的迭代滤波算法拓展至球面域的问题展开探讨。我们回顾了经典迭代滤波方法的性质，提出了其拓展形式，并研究了离散环境下的收敛性。具体而言，通过利用广义局部Toeplitz序列理论，我们能够从谱特征上刻画与迭代滤波球面拓展相关的算子，并给出了其收敛性的反例。最终，我们提出了一种具有收敛性的变体，称为球面迭代滤波，并展示了将其应用于球面数据的数值结果。