Synchrosqueezed Fractional Wavelet Transform: A New High-Resolution Time-Frequency Representation

Jun Shi; Gong Chen; Yanan Zhao; Ran Tao

doi:10.1109/TSP.2023.3244105

Synchrosqueezed Fractional Wavelet Transform: A New High-Resolution Time-Frequency Representation

Jun Shi, Gong Chen^*, Yanan Zhao, Ran Tao^*

^*Corresponding author for this work

School of Information and Electronics

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

The synchrosqueezed wavelet transform (SSWT) has been proven to be a powerful time-frequency analysis tool. However, this transform is unable to deal with signals with fast varying instantaneous frequencies. The objective of this paper is to overcome this deficiency using the fractional wavelet transform (FRWT), which is a generalization of the conventional wavelet transform. We first propose a synchrosqueezed FRWT (SSFRWT), which shares many properties of its SSWT counterpart while offering attractive new features. Then, we present a theoretical analysis of the SSFRWT, including the derivation of its basic properties. Moreover, we show that the discrete form of the SSFRWT admits efficient numerical implementation akin to that of the SSWT. Finally, the theoretical derivations are validated via simulations.

Original language	English
Pages (from-to)	264-278
Number of pages	15
Journal	IEEE Transactions on Signal Processing
Volume	71
DOIs	https://doi.org/10.1109/TSP.2023.3244105
Publication status	Published - 2023

Keywords

Fractional Fourier transform
fractional wavelet transform
non-stationary signals
synchrosqueezed wavelet transform
time-frequency representation

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10.1109/TSP.2023.3244105

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title = "Synchrosqueezed Fractional Wavelet Transform: A New High-Resolution Time-Frequency Representation",

abstract = "The synchrosqueezed wavelet transform (SSWT) has been proven to be a powerful time-frequency analysis tool. However, this transform is unable to deal with signals with fast varying instantaneous frequencies. The objective of this paper is to overcome this deficiency using the fractional wavelet transform (FRWT), which is a generalization of the conventional wavelet transform. We first propose a synchrosqueezed FRWT (SSFRWT), which shares many properties of its SSWT counterpart while offering attractive new features. Then, we present a theoretical analysis of the SSFRWT, including the derivation of its basic properties. Moreover, we show that the discrete form of the SSFRWT admits efficient numerical implementation akin to that of the SSWT. Finally, the theoretical derivations are validated via simulations.",

keywords = "Fractional Fourier transform, fractional wavelet transform, non-stationary signals, synchrosqueezed wavelet transform, time-frequency representation",

author = "Jun Shi and Gong Chen and Yanan Zhao and Ran Tao",

note = "Publisher Copyright: {\textcopyright} 1991-2012 IEEE.",

year = "2023",

doi = "10.1109/TSP.2023.3244105",

language = "English",

volume = "71",

pages = "264--278",

journal = "IEEE Transactions on Signal Processing",

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TY - JOUR

T1 - Synchrosqueezed Fractional Wavelet Transform

T2 - A New High-Resolution Time-Frequency Representation

AU - Shi, Jun

AU - Chen, Gong

AU - Zhao, Yanan

AU - Tao, Ran

PY - 2023

Y1 - 2023

N2 - The synchrosqueezed wavelet transform (SSWT) has been proven to be a powerful time-frequency analysis tool. However, this transform is unable to deal with signals with fast varying instantaneous frequencies. The objective of this paper is to overcome this deficiency using the fractional wavelet transform (FRWT), which is a generalization of the conventional wavelet transform. We first propose a synchrosqueezed FRWT (SSFRWT), which shares many properties of its SSWT counterpart while offering attractive new features. Then, we present a theoretical analysis of the SSFRWT, including the derivation of its basic properties. Moreover, we show that the discrete form of the SSFRWT admits efficient numerical implementation akin to that of the SSWT. Finally, the theoretical derivations are validated via simulations.

AB - The synchrosqueezed wavelet transform (SSWT) has been proven to be a powerful time-frequency analysis tool. However, this transform is unable to deal with signals with fast varying instantaneous frequencies. The objective of this paper is to overcome this deficiency using the fractional wavelet transform (FRWT), which is a generalization of the conventional wavelet transform. We first propose a synchrosqueezed FRWT (SSFRWT), which shares many properties of its SSWT counterpart while offering attractive new features. Then, we present a theoretical analysis of the SSFRWT, including the derivation of its basic properties. Moreover, we show that the discrete form of the SSFRWT admits efficient numerical implementation akin to that of the SSWT. Finally, the theoretical derivations are validated via simulations.

KW - Fractional Fourier transform

KW - fractional wavelet transform

KW - non-stationary signals

KW - synchrosqueezed wavelet transform

KW - time-frequency representation

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DO - 10.1109/TSP.2023.3244105

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JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

ER -

Synchrosqueezed Fractional Wavelet Transform: A New High-Resolution Time-Frequency Representation

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Keywords

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