AnExtendedHilbertTransform

Phase reconstruction from oscillatory data via an extended Hilbert transform (HT) method (Matsuki, Kori and Kobayashi, Sci. Rep., 2023).

Compared to the conventional HT method, the extended HT method can reconstruct phase more accurately from a sinusoidal signal $x(t) = A_L \cos (\hat{\omega} t + u(t))$, where $A_L$ is a slow amplitude and $u(t)$ is a small phase-modulation.

Requirement

• Python 3.8.8
• NumPy 1.20.1
• SciPy 1.6.2
• Matplotlib 3.3.4
• sdeint 0.2.2

Demo

See Demo_An_Extended_Hilbert_Transform.ipynb

Usage

Reconstruct the phase via the conventional and the extended HT method by

python3 main.py "[file name]" tau

• file name: Name of the file(.txt) of the observed signal.
• tau: Sampling interval of the observed signal (float).

For example,

python3 main.py "x_QuasiPeriodic.txt" 0.01

Two files will be generated:

• phase_exth.txt : phase reconstructed via the extended HT method.
• phase_h.txt : phase reconstructed via the conventional HT method.

Author

Akari Matsuki mail to : akarimatsuki114[at]gmail.com