The Synchrosqueezing algorithm for time-varying spectral analysis: Robustness properties and new paleoclimate applications

Gaurav Thakur; Eugene Brevdo; Neven S. Fučkar; Hau Tieng Wu

doi:10.1016/j.sigpro.2012.11.029

The Synchrosqueezing algorithm for time-varying spectral analysis: Robustness properties and new paleoclimate applications

Gaurav Thakur, Eugene Brevdo, Neven S. Fučkar, Hau Tieng Wu

Mathematics

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

Abstract

We analyze the stability properties of the Synchrosqueezing transform, a time-frequency signal analysis method that can identify and extract oscillatory components with time-varying frequency and amplitude. We show that Synchrosqueezing is robust to bounded perturbations of the signal and to Gaussian white noise. These results justify its applicability to noisy or nonuniformly sampled data that is ubiquitous in engineering and the natural sciences. We also describe a practical implementation of Synchrosqueezing and provide guidance on tuning its main parameters. As a case study in the geosciences, we examine characteristics of a key paleoclimate change in the last 2.5 million years, where Synchrosqueezing provides significantly improved insights.

Original language	English (US)
Pages (from-to)	1079-1094
Number of pages	16
Journal	Signal Processing
Volume	93
Issue number	5
DOIs	https://doi.org/10.1016/j.sigpro.2012.11.029
State	Published - May 2013

Keywords

Instantaneous frequency
Nonstationary signal analysis
Synchrosqueezing
Time-frequency reassignment
Time-varying spectrum

ASJC Scopus subject areas

Control and Systems Engineering
Software
Signal Processing
Computer Vision and Pattern Recognition
Electrical and Electronic Engineering

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10.1016/j.sigpro.2012.11.029

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title = "The Synchrosqueezing algorithm for time-varying spectral analysis: Robustness properties and new paleoclimate applications",

abstract = "We analyze the stability properties of the Synchrosqueezing transform, a time-frequency signal analysis method that can identify and extract oscillatory components with time-varying frequency and amplitude. We show that Synchrosqueezing is robust to bounded perturbations of the signal and to Gaussian white noise. These results justify its applicability to noisy or nonuniformly sampled data that is ubiquitous in engineering and the natural sciences. We also describe a practical implementation of Synchrosqueezing and provide guidance on tuning its main parameters. As a case study in the geosciences, we examine characteristics of a key paleoclimate change in the last 2.5 million years, where Synchrosqueezing provides significantly improved insights.",

keywords = "Instantaneous frequency, Nonstationary signal analysis, Synchrosqueezing, Time-frequency reassignment, Time-varying spectrum",

author = "Gaurav Thakur and Eugene Brevdo and Fu{\v c}kar, {Neven S.} and Wu, {Hau Tieng}",

note = "Funding Information: The authors would like to thank Prof. I. Daubechies for many insightful discussions. N.S. Fu{\v c}kar also acknowledges valuable input from Dr. O. Elison Timm and H.T. Wu acknowledges input from Prof. Z. Wu on the use of EEMD. E. Brevdo acknowledges partial support from the NSF GRF grant No. DGE-0646086 . H.-T. Wu and G. Thakur acknowledge partial support from FHWA grant No. DTFH61-08-C-00028 .",

year = "2013",

month = may,

doi = "10.1016/j.sigpro.2012.11.029",

language = "English (US)",

volume = "93",

pages = "1079--1094",

journal = "Signal Processing",

issn = "0165-1684",

publisher = "Elsevier",

number = "5",

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T1 - The Synchrosqueezing algorithm for time-varying spectral analysis

T2 - Robustness properties and new paleoclimate applications

AU - Thakur, Gaurav

AU - Brevdo, Eugene

AU - Fučkar, Neven S.

AU - Wu, Hau Tieng

N1 - Funding Information: The authors would like to thank Prof. I. Daubechies for many insightful discussions. N.S. Fučkar also acknowledges valuable input from Dr. O. Elison Timm and H.T. Wu acknowledges input from Prof. Z. Wu on the use of EEMD. E. Brevdo acknowledges partial support from the NSF GRF grant No. DGE-0646086 . H.-T. Wu and G. Thakur acknowledge partial support from FHWA grant No. DTFH61-08-C-00028 .

PY - 2013/5

Y1 - 2013/5

N2 - We analyze the stability properties of the Synchrosqueezing transform, a time-frequency signal analysis method that can identify and extract oscillatory components with time-varying frequency and amplitude. We show that Synchrosqueezing is robust to bounded perturbations of the signal and to Gaussian white noise. These results justify its applicability to noisy or nonuniformly sampled data that is ubiquitous in engineering and the natural sciences. We also describe a practical implementation of Synchrosqueezing and provide guidance on tuning its main parameters. As a case study in the geosciences, we examine characteristics of a key paleoclimate change in the last 2.5 million years, where Synchrosqueezing provides significantly improved insights.

AB - We analyze the stability properties of the Synchrosqueezing transform, a time-frequency signal analysis method that can identify and extract oscillatory components with time-varying frequency and amplitude. We show that Synchrosqueezing is robust to bounded perturbations of the signal and to Gaussian white noise. These results justify its applicability to noisy or nonuniformly sampled data that is ubiquitous in engineering and the natural sciences. We also describe a practical implementation of Synchrosqueezing and provide guidance on tuning its main parameters. As a case study in the geosciences, we examine characteristics of a key paleoclimate change in the last 2.5 million years, where Synchrosqueezing provides significantly improved insights.

KW - Instantaneous frequency

KW - Nonstationary signal analysis

KW - Synchrosqueezing

KW - Time-frequency reassignment

KW - Time-varying spectrum

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JO - Signal Processing

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IS - 5

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The Synchrosqueezing algorithm for time-varying spectral analysis: Robustness properties and new paleoclimate applications

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Keywords

ASJC Scopus subject areas

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