A Second-Order Synchrosqueezing Transform with a Simple Form of Phase Transformation

A Second-Order Synchrosqueezing Transform with a Simple Form of Phase Transformation

Year:    2021

Author:    Jawaher H. Alzahrani, Jian Lu, Qingtang Jiang, Jawaher H. Alzahrani, Qingtang Jiang

Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 3 : pp. 624–649

Abstract

To model a non-stationary signal as a superposition of amplitude and frequency-modulated Fourier-like oscillatory modes is important to extract information, such as the underlying dynamics, hidden in the signal. Recently, the synchrosqueezed wavelet transform (SST) and its variants have been developed to estimate instantaneous frequencies and separate the components of non-stationary multicomponent signals. The short-time Fourier transform-based SST (FSST for short) reassigns the frequency variable to sharpen the time-frequency representation and to separate the components of a multicomponent non-stationary signal. However, FSST works well only with multicomponent signals having slowly changing frequencies. To deal with multicomponent signals having fast-changing frequencies, the second-order FSST (FSST2 for short) was proposed. The key point for FSST2 is to construct a phase transformation of a signal which is the instantaneous frequency when the signal is a linear chirp. In this paper we consider a phase transformation for FSST2 which has a simpler expression than that used in the literature. In the study the theoretical analysis of FSST2 with this phase transformation, we observe that the proof for the error bounds for the instantaneous frequency estimation and component recovery is simpler than that with the conventional phase transformation. We also provide some experimental results which show that this FSST2 performs well in non-stationary multicomponent signal separation.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2020-0077

Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 3 : pp. 624–649

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords:    Short-time Fourier transform second-order synchrosqueezing transform phase transformation instantaneous frequency estimation multicomponent signal separation.

Author Details

Jawaher H. Alzahrani

Jian Lu

Qingtang Jiang

Jawaher H. Alzahrani

Qingtang Jiang

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