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Defining the Wavelet Bispectrum

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Defining the Wavelet Bispectrum. / Newman, Julian; Pidde, Aleksandra; Stefanovska, Aneta.
In: Applied and Computational Harmonic Analysis, Vol. 51, 31.03.2021, p. 171-224.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Newman, J, Pidde, A & Stefanovska, A 2021, 'Defining the Wavelet Bispectrum', Applied and Computational Harmonic Analysis, vol. 51, pp. 171-224. https://doi.org/10.1016/j.acha.2020.10.005

APA

Vancouver

Newman J, Pidde A, Stefanovska A. Defining the Wavelet Bispectrum. Applied and Computational Harmonic Analysis. 2021 Mar 31;51:171-224. Epub 2020 Nov 5. doi: 10.1016/j.acha.2020.10.005

Author

Newman, Julian ; Pidde, Aleksandra ; Stefanovska, Aneta. / Defining the Wavelet Bispectrum. In: Applied and Computational Harmonic Analysis. 2021 ; Vol. 51. pp. 171-224.

Bibtex

@article{a2c85215610c4d43a01e7cedb20347e0,
title = "Defining the Wavelet Bispectrum",
abstract = "Bispectral analysis is an eective signal processing tool for analysing interactions between oscillations, and has been adapted to the continuous wavelet transform for time-evolving analysis of open systems. However, one unaddressed question for the wavelet bispectrum is quantication of the bispectral content of an area of scale-scale space. This makes the capacity for quantitative rather than merely qualitative interpretation of wavelet bispectrum computations very limited. In this paper, we overcome this limitation by providing suitable normalisations of the wavelet bispectrum formula that enable it to be treated as a density to be integrated. These are roughly analogous to the normalisation for second-order wavelet spectral densities. We prove that our denition of the wavelet bispectrum matches the traditional bispectrum of sums of sinusoids, in the limit as the frequency resolution tends to innity. We illustrate the improved quantitative power of our denition with numerical and experimental data.",
keywords = "continuous wavelet transform, wavelet bispectrum, bispectral analysis, time-frequency analysis, lognormal wavelets",
author = "Julian Newman and Aleksandra Pidde and Aneta Stefanovska",
year = "2021",
month = mar,
day = "31",
doi = "10.1016/j.acha.2020.10.005",
language = "English",
volume = "51",
pages = "171--224",
journal = "Applied and Computational Harmonic Analysis",
issn = "1063-5203",
publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - Defining the Wavelet Bispectrum

AU - Newman, Julian

AU - Pidde, Aleksandra

AU - Stefanovska, Aneta

PY - 2021/3/31

Y1 - 2021/3/31

N2 - Bispectral analysis is an eective signal processing tool for analysing interactions between oscillations, and has been adapted to the continuous wavelet transform for time-evolving analysis of open systems. However, one unaddressed question for the wavelet bispectrum is quantication of the bispectral content of an area of scale-scale space. This makes the capacity for quantitative rather than merely qualitative interpretation of wavelet bispectrum computations very limited. In this paper, we overcome this limitation by providing suitable normalisations of the wavelet bispectrum formula that enable it to be treated as a density to be integrated. These are roughly analogous to the normalisation for second-order wavelet spectral densities. We prove that our denition of the wavelet bispectrum matches the traditional bispectrum of sums of sinusoids, in the limit as the frequency resolution tends to innity. We illustrate the improved quantitative power of our denition with numerical and experimental data.

AB - Bispectral analysis is an eective signal processing tool for analysing interactions between oscillations, and has been adapted to the continuous wavelet transform for time-evolving analysis of open systems. However, one unaddressed question for the wavelet bispectrum is quantication of the bispectral content of an area of scale-scale space. This makes the capacity for quantitative rather than merely qualitative interpretation of wavelet bispectrum computations very limited. In this paper, we overcome this limitation by providing suitable normalisations of the wavelet bispectrum formula that enable it to be treated as a density to be integrated. These are roughly analogous to the normalisation for second-order wavelet spectral densities. We prove that our denition of the wavelet bispectrum matches the traditional bispectrum of sums of sinusoids, in the limit as the frequency resolution tends to innity. We illustrate the improved quantitative power of our denition with numerical and experimental data.

KW - continuous wavelet transform

KW - wavelet bispectrum

KW - bispectral analysis

KW - time-frequency analysis

KW - lognormal wavelets

U2 - 10.1016/j.acha.2020.10.005

DO - 10.1016/j.acha.2020.10.005

M3 - Journal article

VL - 51

SP - 171

EP - 224

JO - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

SN - 1063-5203

ER -