Document Type

Dissertation

Degree

Doctor of Philosophy

Major

Mathematics

Date of Defense

3-12-2020

Graduate Advisor

Qingtang Jiang

Committee

Haiyan Cai

Wenjie He

Yuefeng Wu

Abstract

The prevalence of the separation of multicomponent non-stationary signals across many elds of research makes this concept an important subject of study. The synchrosqueezing transform (SST) is a particular type of reassignment method. It aims to separate and recover the components of a multicomponent non-stationary signal. The short time Fourier transform (STFT)-based SST (FSST) and the continuous wavelet transform (CWT)based SST (WSST) have been used in engineering and medical data analysis applications. The current study introduces the dierent versions of FSST and WSST to estimate instantaneous frequency (IF) and to recover components. It has a good concentration and reconstruction for a wide variety of amplitude and frequency modulated multicomponent signals. Earlier studies have improved existing FSSTs by computing more accurate estimates of the IFs of the modes making up the signal. The higher order approximations for both the amplitude and phase were used. Therefore, there is a better concentration and reconstruction for a wider variety of AM-FM modes than what was possible with current synchrosqueezing techniques. In this study, we propose to improve the adaptive FSST, the adaptive WSST, and to introduce a new type of 2nd-order FSST with a new phase transformation. We use higher order approximations for both the amplitude and phase function. We study the higher order adaptive FSST and adaptive WSST. The result shows an even better concentration and reconstruction for a wider variety of AM-FM modes with the higher order adaptive SSTs. We also study the theoretical analysis of the 2nd-order FSST with a new phase transformation. The new phase transformation introduced by us is much simpler than the convectional one, while the performance in IF estimation and component recovery of the new 2nd-order FSST is comparable with, and even better in some cases than, that of the conventional 2nd-order FSST.

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