论文标题
自适应局部迭代过滤和筛选方法的收敛分析
Convergence analysis of Adaptive Locally Iterative Filtering and SIFT method
论文作者
论文摘要
自适应局部迭代过滤（ALIF）是当前提出的新型时频分析工具。经验证明，Alif能够分离组件并克服模式混合问题。但是，到目前为止，其收敛性仍然是一个空旷的问题，尤其是对于高度非平稳的信号，因为与Alif相关的内核是非翻译不变的，非斜率和非对称的事实。我们在这项工作中的第一个贡献是提供对Alif的融合分析。从实际的角度来看，Alif取决于可以实现分解的稳健频率估计器。 我们的第二个贡献是提出一种嘈杂和非组织信号的强大而适应性的分解方法，我们创造了同步性迭代过滤技术（SIFT）。在SIFT中，我们应用同步转换来估计瞬时频率，然后应用ALIF分解信号。我们以数值方式显示了这种新方法处理高度非平稳信号的能力。
Adaptive Local Iterative Filtering (ALIF) is a currently proposed novel time-frequency analysis tool. It has been empirically shown that ALIF is able to separate components and overcome the mode-mixing problem. However, so far its convergence is still an open problem, particularly for highly nonstationary signals, due to the fact that the kernel associated with ALIF is non-translational invariant, non-convolutional and non-symmetric. Our first contribution in this work is providing a convergence analysis of ALIF. From the practical perspective, ALIF depends on a robust frequencies estimator, based on which the decomposition can be achieved. Our second contribution is proposing a robust and adaptive decomposition method for noisy and nonstationary signals, which we coined the Synchrosqueezing Iterative Filtering Technique (SIFT). In SIFT, we apply the synchrosqueezing transform to estimate the instantaneous frequency, and then apply the ALIF to decompose a signal. We show numerically the ability of this new approach in handling highly nonstationary signals.
