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Synchroextracting transform: The theory analysis and comparisons with the synchrosqueezing transform

机译：同步提取变换：与同步压缩变换的理论分析和比较

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摘要

In this paper, we consider the theoretical analysis and new view of a time-frequency analysis method termed synchroextracting transform (SET), which is inspired by the Fourier-based synchrosqueezing transform (FSST) and the ideal time-frequency analysis theory. We first review the corresponding definitions of the FSST and SET. Then, we provide the theoretical analysis of the SET and study some properties with mathematical proofs. We show that the SET mainly benefits from the synchroextracting operator (SEO) that can only retain the TF information most related to time-varying features of the signal. We also give a new view that SEO is equivalent to the fixed frequencies of the frequency estimation operator of the FSST. Based on the SEO, SET greatly improves the concentration of the time-frequency representation and perfectly localizes the time-frequency features of chirp signals. Finally, numerical simulations are employed to illustrate the performance comparisons of the SET and FSST. (C) 2019 Elsevier B.V. All rights reserved.
机译：在本文中，我们考虑了时频分析方法的理论分析和新观点，该方法称为同步提取变换（SET），该方法受到基于傅立叶的同步压缩变换（FSST）和理想时频分析理论的启发。我们首先查看FSST和SET的相应定义。然后，我们对SET进行了理论分析，并通过数学证明研究了一些性质。我们显示SET主要受益于同步提取算子（SEO），该算子只能保留与信号的时变特征最相关的TF信息。我们还给出了一个新观点，即SEO等同于FSST频率估算算符的固定频率。 SET基于SEO，极大地提高了时频表示的集中度，并完美地定位了线性调频信号的时频特征。最后，采用数值模拟来说明SET和FSST的性能比较。 （C）2019 Elsevier B.V.保留所有权利。

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