A better way to define and describe Morlet wavelets for time-frequency analysis

Complex Morlet wavelets are frequently used for time-frequency analysis of non-stationary time series data, such as neuroelectrical signals recorded from the brain. The crucial parameter of Morlet wavelets is the width of the Gaussian that tapers the sine wave. This width parameter controls the trad...

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Vydané v:	NeuroImage (Orlando, Fla.) Ročník 199; s. 81 - 86
Hlavný autor:	Cohen, Michael X
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	United States Elsevier Inc 01.10.2019 Elsevier Limited
Predmet:	Cerebral Cortex - physiology Data analysis Data Interpretation, Statistical Electroencephalography - methods Fourier transforms Frequency dependence Functional Neuroimaging - methods Humans Models, Theoretical Researchers Time series
ISSN:	1053-8119, 1095-9572, 1095-9572
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Abstract	Complex Morlet wavelets are frequently used for time-frequency analysis of non-stationary time series data, such as neuroelectrical signals recorded from the brain. The crucial parameter of Morlet wavelets is the width of the Gaussian that tapers the sine wave. This width parameter controls the trade-off between temporal precision and spectral precision. It is typically defined as the “number of cycles,” but this parameter is opaque, and often leads to uncertainty and suboptimal analysis choices, as well as being difficult to interpret and evaluate. The purpose of this paper is to present alternative formulations of Morlet wavelets in time and in frequency that allow parameterizing the wavelets directly in terms of the desired temporal and spectral smoothing (expressed as full-width at half-maximum). This formulation provides clarity on an important data analysis parameter, and can facilitate proper analyses, reporting, and interpretation of results. MATLAB code and sample data are provided. •Morlet wavelets are used for time-frequency analysis.•The width parameter is usually defined as number-of-cycles.•Alternative formulas are presented here that use full-width at half-maximum.•These formulas will increase clarity of time-frequency analyses and results.
AbstractList	Complex Morlet wavelets are frequently used for time-frequency analysis of non-stationary time series data, such as neuroelectrical signals recorded from the brain. The crucial parameter of Morlet wavelets is the width of the Gaussian that tapers the sine wave. This width parameter controls the trade-off between temporal precision and spectral precision. It is typically defined as the “number of cycles,” but this parameter is opaque, and often leads to uncertainty and suboptimal analysis choices, as well as being difficult to interpret and evaluate. The purpose of this paper is to present alternative formulations of Morlet wavelets in time and in frequency that allow parameterizing the wavelets directly in terms of the desired temporal and spectral smoothing (expressed as full-width at half-maximum). This formulation provides clarity on an important data analysis parameter, and can facilitate proper analyses, reporting, and interpretation of results. MATLAB code and sample data are provided. Complex Morlet wavelets are frequently used for time-frequency analysis of non-stationary time series data, such as neuroelectrical signals recorded from the brain. The crucial parameter of Morlet wavelets is the width of the Gaussian that tapers the sine wave. This width parameter controls the trade-off between temporal precision and spectral precision. It is typically defined as the “number of cycles,” but this parameter is opaque, and often leads to uncertainty and suboptimal analysis choices, as well as being difficult to interpret and evaluate. The purpose of this paper is to present alternative formulations of Morlet wavelets in time and in frequency that allow parameterizing the wavelets directly in terms of the desired temporal and spectral smoothing (expressed as full-width at half-maximum). This formulation provides clarity on an important data analysis parameter, and can facilitate proper analyses, reporting, and interpretation of results. MATLAB code and sample data are provided. •Morlet wavelets are used for time-frequency analysis.•The width parameter is usually defined as number-of-cycles.•Alternative formulas are presented here that use full-width at half-maximum.•These formulas will increase clarity of time-frequency analyses and results. Complex Morlet wavelets are frequently used for time-frequency analysis of non-stationary time series data, such as neuroelectrical signals recorded from the brain. The crucial parameter of Morlet wavelets is the width of the Gaussian that tapers the sine wave. This width parameter controls the trade-off between temporal precision and spectral precision. It is typically defined as the "number of cycles," but this parameter is opaque, and often leads to uncertainty and suboptimal analysis choices, as well as being difficult to interpret and evaluate. The purpose of this paper is to present alternative formulations of Morlet wavelets in time and in frequency that allow parameterizing the wavelets directly in terms of the desired temporal and spectral smoothing (expressed as full-width at half-maximum). This formulation provides clarity on an important data analysis parameter, and can facilitate proper analyses, reporting, and interpretation of results. MATLAB code and sample data are provided.Complex Morlet wavelets are frequently used for time-frequency analysis of non-stationary time series data, such as neuroelectrical signals recorded from the brain. The crucial parameter of Morlet wavelets is the width of the Gaussian that tapers the sine wave. This width parameter controls the trade-off between temporal precision and spectral precision. It is typically defined as the "number of cycles," but this parameter is opaque, and often leads to uncertainty and suboptimal analysis choices, as well as being difficult to interpret and evaluate. The purpose of this paper is to present alternative formulations of Morlet wavelets in time and in frequency that allow parameterizing the wavelets directly in terms of the desired temporal and spectral smoothing (expressed as full-width at half-maximum). This formulation provides clarity on an important data analysis parameter, and can facilitate proper analyses, reporting, and interpretation of results. MATLAB code and sample data are provided.
Author	Cohen, Michael X
Author_xml	– sequence: 1 givenname: Michael X surname: Cohen fullname: Cohen, Michael X email: mikexcohen@gmail.com organization: Radboud University and Radboud University Medical Center, Donders Institute for Neuroscience, the Netherlands
BackLink	https://www.ncbi.nlm.nih.gov/pubmed/31145982$$D View this record in MEDLINE/PubMed
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Copyright	2019 Elsevier Inc. Copyright © 2019 Elsevier Inc. All rights reserved. 2019. Elsevier Inc.
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References	Bruns (bib1) 2004; 137 Cohen (bib3) 2014 Jones (bib5) 2016; 40 Cole, Voytek (bib4) 2017; 21 Cohen (bib2) 2015; 97 Tallon-Baudry, Bertrand (bib6) 1999; 3 Cohen (10.1016/j.neuroimage.2019.05.048_bib2) 2015; 97 Cohen (10.1016/j.neuroimage.2019.05.048_bib3) 2014 Bruns (10.1016/j.neuroimage.2019.05.048_bib1) 2004; 137 Jones (10.1016/j.neuroimage.2019.05.048_bib5) 2016; 40 Cole (10.1016/j.neuroimage.2019.05.048_bib4) 2017; 21 Tallon-Baudry (10.1016/j.neuroimage.2019.05.048_bib6) 1999; 3
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Snippet	Complex Morlet wavelets are frequently used for time-frequency analysis of non-stationary time series data, such as neuroelectrical signals recorded from the...
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SubjectTerms	Cerebral Cortex - physiology Data analysis Data Interpretation, Statistical Electroencephalography - methods Fourier transforms Frequency dependence Functional Neuroimaging - methods Humans Models, Theoretical Researchers Time series
Title	A better way to define and describe Morlet wavelets for time-frequency analysis
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