自适应局部迭代滤波与SIFT方法的收敛性分析
Convergence analysis of Adaptive Locally Iterative Filtering and SIFT method
摘要：
自适应局部迭代滤波（ALIF）是目前提出的一种新的时频分析工具。经验表明，ALIF能够分离组分并克服模式混合问题。然而，到目前为止，它的收敛仍然是一个悬而未决的问题，特别是对于高度非平稳信号，由于与ALIF相关的内核是非平移不变，非卷积和非对称的事实。我们在这项工作中的第一个贡献是提供ALIF的收敛性分析。从实际的角度来看，ALIF依赖于一个强大的频率估计，基于该分解可以实现。我们的第二个贡献是提出了一个强大的和自适应的分解方法的噪声和非平稳信号，我们创造了同步压缩迭代滤波技术（SIFT）。在SIFT中，我们应用同步压缩变换来估计瞬时频率，然后应用ALIF来分解信号。我们数值显示这种新方法在处理高度非平稳信号的能力。
英文摘要：
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.
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