数学与统计学院学术报告[2023] 053号

(高水平大学建设系列报告824号)

报告题目: Time-frequency Methods for Separation of Non-stationary Multi-component Signals

报告人：蒋庆堂教授 （University of Missouri-St. Louis）

报告时间：2023年7月17日16:30-17:30

报告地点：汇星楼514 　　　　　　　　　　　　　　　　　　　　　　　　

报告内容：Most real-world signals appear as multi-component signals. To facilitate processing the signals, the unknown components of the multi-component signal of interest should be extracted from the blind-source data. However, for non-stationary signals (i.e. with frequencies of the components being functions of the time variable), there has been no rigorous mathematical approach available, till the introduction of the synchrosqueezing transform (SST), by Ingrid Daubechies and her collaborators a decade ago. Unfortunately, even with the efforts by many researchers, SST applies only under very restrictive specifications. In this presentation, we will discuss two improvements of SST. Firstly, a direct time-frequency method with a linear chirp local approximation is introduced to remove some of the restrictions for more accurate component recovery. Secondly, we will discuss chirplet transform and our most recently developed time-scale-chrip_rate (TSC_R) approach to separate multi-component signals even with crossover instantaneous frequency curves. TSC_R (chirplet transform resp) maps a signal into a 3-dimensional space of time, scale (frequency resp) and chirp-rate, as opposed to the traditional 2-dimensional space of time and scale (or frequency). Demonstrative examples will also be presented.

报告人简历：蒋庆堂教授是国际著名小波分析的专家，博士毕业于北京大学，1997年与北京大学的彭立中教授合作开展小波分析的研究，现在美国University of Missouri-St. Louis的数学与计算机系任教，在国内外发表众多学术著作，并担任多本数学国际期刊的编辑。

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　　　　　　　　　　　　　　　　　　　2023年7月13日