基于解析信号重构的同步挤压小波变换的时频谱影响因素分析

Analysis of the Influence Factors on the Time-Frequency Spectrum Obtained by Synchrosqueezing Wavelet Transform based on Reconstruction of Analytic Signal

受测不准原理的制约,小波变换、S变换等时频分析算法无法同时获得高时间分辨率和高频率分辨率。为了满足更高的要求,出现了一种联合小波变换和时频谱重组的新方法—同步挤压小波变换。本文从同步挤压小波变换和基于解析信号重构的同步挤压小波变换的原理出发,通过模型分析算法中参数设置对时频分析结果的影响,包括小波母函数、小波母函数的参数选择和小波阈值等,分析瞬时频率变化率不为零的信号所存在的时频谱模糊现象,并通过控制小波母函数、小波母函数参数以及小波阈值有效地减轻瞬时频率变化率不为零的信号所存在的时频谱模糊现象,时频谱的质量得到一定程度的提高。研究结果对获取高分辨率地震时频谱具有一定的指导意义。

Because of the limitation of Heisenberg＇s uncertainty principle, the algorithms of time-frequency spectrum decomposition, for example, wavelet transform, and S transform, cannot simultaneously have high resolution in time and frequency domain. In order to meet the higher requirements, there appeared a new method that combined wavelet transform with the time-frequency spectrum rearrangement, which is called synchrosqueezing wavelet transform. In this paper, the related parameters of the algorithm which affect the results of the time-frequency analysis, such as wavelet mother function and its parameter selection, wavelet threshold, are studied. The time-frequency spectrum ambiguity has been analyzed when the variation rate of instantaneous frequency of the signal not equals to zero. The generalized synchrosqueezing wavelet transform algorithm is studied, and the quality of time-frequency spectrum is improved to a certain degree. This result has a certain guiding significance for achieving high resolution time-frequency spectrum.