Phase reconstruction from oscillatory data with iterated Hilbert transform embeddings
- In the data analysis of oscillatory systems, methods based on phase reconstruction are widely used to characterize phase-locking properties and inferring the phase dynamics. The main component in these studies is an extraction of the phase from a time series of an oscillating scalar observable. We discuss a practical procedure of phase reconstruction by virtue of a recently proposed method termed iterated Hilbert transform embeddings. We exemplify the potential benefits and limitations of the approach by applying it to a generic observable of a forced Stuart-Landau oscillator. Although in many cases, unavoidable amplitude modulation of the observed signal does not allow for perfect phase reconstruction, in cases of strong stability of oscillations and a high frequency of the forcing, iterated Hilbert transform embeddings significantly improve the quality of the reconstructed phase. We also demonstrate that for significant amplitude modulation, iterated embeddings do not provide any improvement.
Author details: | Erik GengelORCiDGND, Arkadij PikovskijORCiDGND |
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DOI: | https://doi.org/10.1016/j.physd.2021.133070 |
ISSN: | 0167-2789 |
ISSN: | 1872-8022 |
Title of parent work (English): | Physica : D, Nonlinear phenomena |
Subtitle (English): | benefits and limitations |
Publisher: | Elsevier |
Place of publishing: | Amsterdam |
Publication type: | Article |
Language: | English |
Date of first publication: | 2021/10/23 |
Publication year: | 2022 |
Release date: | 2024/03/28 |
Tag: | Data analysis; Hilbert transform; Phase reconstruction |
Volume: | 429 |
Article number: | 133070 |
Number of pages: | 9 |
Funding institution: | Friedrich-Ebert Stiftung; Potsdam Graduate School; Russian Science FoundationRussian Science Foundation (RSF) [17-12-01534]; Russian Ministry of Science and Higher Education [075-15-2019-1931] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |