一种用于瞬态信号时频分析的能量集中小波变换
An Energy-concentrated Wavelet Transform for Time Frequency Analysis of Transient Signals
摘要：
瞬态信号往往由一系列具有多值瞬时频率（IF）的模态组成，这给信号处理技术的发展带来了挑战。幸运的是，这种信号的群延迟（GD）可以很好地表示为频率的单值函数。针对频域信号模型，提出了一种基于小波变换的时间重分配同步压缩变换后处理方法。我们提出的方法嵌入一个二维GD算子到同步压缩框架中，以产生具有高能量集中的瞬态信号的时频表示（TFR），并允许检索整个或部分信号。给出了WTSST的理论分析，包括GD候选精度和信号重构精度的分析。在WTSST的基础上，通过引入一种逐步细化方案，提出了基于WT的时间重分配多同步压缩变换（WTMSST），进一步改善了WTSST方法不能处理强频变信号的缺点.仿真和实际信号分析表明，所提出的方法能够较好地描述瞬态信号的特征。
英文摘要：
Transient signals are often composed of a series of modes that have multivalued time-dependent instantaneous frequency (IF), which brings challenges to the development of signal processing technology. Fortunately, the group delay (GD) of such signal can be well expressed as a single valued function of frequency. By considering the frequency-domain signal model, we present a postprocessing method called wavelet transform (WT)-based time-reassigned synchrosqueezing transform (WTSST). Our proposed method embeds a two-dimensional GD operator into a synchrosqueezing framework to generate a time-frequency representation (TFR) of transient signal with high energy concentration and allows to retrieve the whole or part of the signal. The theoretical analyses of the WTSST are provided, including the analysis of GD candidate accuracy and signal reconstruction accuracy. Moreover, based on WTSST, the WT-based time-reassigned multisynchrosqueezing transform (WTMSST) is proposed by introducing a stepwise refinement scheme, which further improves the drawback that the WTSST method is unable to deal with strong frequency-varying signal. Simulation and real signal analysis illustrate that the proposed methods have the capacity to appropriately describe the features of transient signals.
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