Hamilton, J., Nunes, M.A., Knight, Marina Iuliana orcid.org/0000-0001-9926-6092 et al. (1 more author) (2017) Complex-valued wavelet lifting and applications. Technometrics. pp. 48-60. ISSN 1537-2723
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. Supplementary materials for this article are available online.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details |
Keywords: | (Bivariate) time series,Coherence and phase,Lifting scheme,Nondecimated transform,Nonparametric regression,Wavelets |
Dates: |
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Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Mathematics (York) |
Depositing User: | Pure (York) |
Date Deposited: | 18 Jan 2017 10:10 |
Last Modified: | 13 Mar 2025 05:23 |
Published Version: | https://doi.org/10.1080/00401706.2017.1281846 |
Status: | Published |
Refereed: | Yes |
Identification Number: | 10.1080/00401706.2017.1281846 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:110760 |
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