hhtpy

An Empirical Mode Decomposition (EMD) implementation in Python.

Overview

hhtpy is a Python library for performing Empirical Mode Decomposition (EMD) on one-dimensional signals. EMD is a key part of the Hilbert-Huang Transform (HHT), which is used for analyzing nonlinear and non-stationary time series data.

This library was written by Lars Havstad and Geir Kulia.

Usage

Here's a basic example of how to use hhtpy to perform EMD on a signal:

import numpy as np
import matplotlib.pyplot as plt
from hhtpy import hilbert_huang_transform
from hhtpy.plot import plot_imfs, plot_hilbert_spectrum


T = 5  # sec
f_s = 15000  # Hz
n = np.arange(T * f_s)
t = n / f_s  # sec

y = 1 * np.cos(2 * np.pi * 50 * t + 20 * np.sin(2 * np.pi * 0.5 * t)) + 2 * np.cos(
    2 * np.pi * 20 * t
)

imfs, residue = hilbert_huang_transform(y, f_s)

fig, axs = plot_imfs(imfs, y, residue, t, max_number_of_imfs=2)

fig, ax, clb = plot_hilbert_spectrum(
    imfs,
    max_number_of_imfs=2,
)

fig, ax = plot_marginal_hilbert_spectrum(imfs)

Custom Stopping Criterion

You can provide a custom stopping criterion function to control the sifting process. The function should accept the current mode and total sifts performed as input and return a boolean indicating whether to stop sifting (True) or continue (False).

def custom_stopping_criterion(mode: np.ndarray, total_sifts_performed:int) -> bool:
    # Your custom logic here
    return True  # or False

Acknowledgements

We want to express our sincere gratitude to the following individuals for their invaluable contributions and support throughout this project:

• Professor Norden Huang: For his extensive one-on-one lectures over ten days, during which he taught us the Hilbert-Huang Transform (HHT) and guided us through the nuances of implementing it. Many of the insights and implementation techniques used in this project directly result from these invaluable sessions.

• Professor Marta Molinas: To introduce us to the HHT methodology, provide foundational knowledge, and engage in valuable discussions about the implementation. Her guidance has been instrumental in shaping our understanding and approach.

• Professor Olav B. Fosso: For his numerous fruitful dialogues on improving and optimizing the algorithm. His insights have greatly influenced the refinement of our implementation.

• Sumit Kumar Ram (@sumitram): For explaining the HHT algorithm to me for the first time. His clear and concise explanation provided the initial spark that fueled our deeper exploration of the method.

Thank you all for your expertise, time, and mentorship, which made this work possible.

Contributing

Contributions are welcome! If you have suggestions for improvements or find any issues, please open an issue or submit a pull request on the GitHub repository.