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Volume 14, Issue 3
A Second-Order Synchrosqueezing Transform with a Simple Form of Phase Transformation

Jian Lu, Jawaher H. Alzahrani & Qingtang Jiang

Numer. Math. Theor. Meth. Appl., 14 (2021), pp. 624-649.

Published online: 2021-06

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  • 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.

  • AMS Subject Headings

42C15, 42A38

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-14-624, author = {Lu , JianAlzahrani , Jawaher H. and Jiang , Qingtang}, title = {A Second-Order Synchrosqueezing Transform with a Simple Form of Phase Transformation}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2021}, volume = {14}, number = {3}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2020-0077}, url = {http://global-sci.org/intro/article_detail/nmtma/19192.html} }
TY - JOUR T1 - A Second-Order Synchrosqueezing Transform with a Simple Form of Phase Transformation AU - Lu , Jian AU - Alzahrani , Jawaher H. AU - Jiang , Qingtang JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 624 EP - 649 PY - 2021 DA - 2021/06 SN - 14 DO - http://doi.org/10.4208/nmtma.OA-2020-0077 UR - https://global-sci.org/intro/article_detail/nmtma/19192.html KW - Short-time Fourier transform, second-order synchrosqueezing transform, phase transformation, instantaneous frequency estimation, multicomponent signal separation. AB -

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.

Jian Lu, Jawaher H. Alzahrani & Qingtang Jiang. (2021). A Second-Order Synchrosqueezing Transform with a Simple Form of Phase Transformation. Numerical Mathematics: Theory, Methods and Applications. 14 (3). 624-649. doi:10.4208/nmtma.OA-2020-0077
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