TY  - JOUR
A1  - Gengel, Erik
A1  - Pikovskij, Arkadij
T1  - Phase reconstruction from oscillatory data with iterated Hilbert transform embeddings
T2  - Physica : D, Nonlinear phenomena
N2  - 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.
KW  - Data analysis
KW  - Phase reconstruction
KW  - Hilbert transform
Y1  - 2021
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/63086
SN  - 0167-2789
SN  - 1872-8022
VL  - 429
PB  - Elsevier
CY  - Amsterdam
ER  -