Dissemin is shutting down on January 1st, 2025

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Nature Research, Scientific Reports, 1(13), 2023

DOI: 10.1038/s41598-023-30405-5

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An extended Hilbert transform method for reconstructing the phase from an oscillatory signal

Journal article published in 2023 by Akari Matsuki, Hiroshi Kori, Ryota Kobayashi ORCID
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

AbstractRhythmic activity is ubiquitous in biological systems from the cellular to organism level. Reconstructing the instantaneous phase is the first step in analyzing the essential mechanism leading to a synchronization state from the observed signals. A popular method of phase reconstruction is based on the Hilbert transform, which can only reconstruct the interpretable phase from a limited class of signals, e.g., narrow band signals. To address this issue, we propose an extended Hilbert transform method that accurately reconstructs the phase from various oscillatory signals. The proposed method is developed by analyzing the reconstruction error of the Hilbert transform method with the aid of Bedrosian’s theorem. We validate the proposed method using synthetic data and show its systematically improved performance compared with the conventional Hilbert transform method with respect to accurately reconstructing the phase. Finally, we demonstrate that the proposed method is potentially useful for detecting the phase shift in an observed signal. The proposed method is expected to facilitate the study of synchronization phenomena from experimental data.