Hamilton, J. orcid.org/0000-0003-3326-9842, Nunes, M.A., Knight, M.I. et al. (1 more author) (2017) Complex-valued wavelet lifting and applications. Technometrics. ISSN 0040-1706
Abstract
Signals with irregular sampling structures arise naturally in many fields. In applications such as spectral decomposition and nonparametric regression, classical methods often assume a regular sampling pattern, thus cannot be applied without prior data processing. This work proposes new complex-valued analysis techniques based on the wavelet lifting scheme that removes ‘one coefficient at a time’. Our proposed lifting transform can be applied directly to irregularly sampled data and is able to adapt to the signal(s)’ characteristics. As our new lifting scheme produces complex-valued wavelet coefficients, it provides an alternative to the Fourier transform for irregular designs, allowing phase or directional information to be represented. We discuss applications in bivariate time series analysis, where the complex-valued lifting construction allows for coherence and phase quantification. We also demonstrate the potential of this flexible methodology over real-valued analysis in the nonparametric regression context.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 Taylor and Francis. This is an author produced version of a paper subsequently published in Technometrics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | lifting scheme; wavelets; nondecimated transform; (bivariate) time series; coherence and phase; nonparametric regression |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Medicine, Dentistry and Health (Sheffield) > School of Health and Related Research (Sheffield) > ScHARR - Sheffield Centre for Health and Related Research |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 09 Feb 2017 11:44 |
Last Modified: | 17 Jul 2018 00:38 |
Published Version: | https://doi.org/10.1080/00401706.2017.1281846 |
Status: | Published |
Publisher: | Taylor & Francis |
Refereed: | Yes |
Identification Number: | 10.1080/00401706.2017.1281846 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:111876 |