Hyperbolic S-Transform

Package for Hyperbolic S-transform. Link to Pypi Project

1. Introduction

HS Transform is a Python package for performing Hyperbolic S-transform [1]. The S-transform is a time-frequency representation that combines the best properties of the Short-time Fourier Transform and the Wavelet Transform. It provides simultaneous information on both the frequency content and temporal localization of a signal.

This is a work of my published paper

References

[1] Stockwell, R.G., Mansinha, L. & Lowe, R.P., (1996). Localization of the complex spectrum: the S transform. IEEE Trans. Signal Process., 44(4), 998–1001, doi:10.1109/78.492555

2. Dependencies

HS Transform requires the following Python packages:

• numpy
• scipy
• pandas
• matplotlib
• pytest

3. How to Install

After that, you can install HS Transform using pip:

pip install HSTransform

You can also install all dependencies and package in 1 statement

pip install numpy scipy pandas matplotlib pytest HSTransform

4. Run tests

After installation, you can test the package using the included test scripts: pytest tests/

5. Example

Here’s an example of how to use HS Transform to analyze a signal with voltage disturbance and power system fault:

It's noted sometimes you need to include the installed HSTransform package location into sys

import sys
import os

# Add the package directory to sys.path
package_path = os.path.abspath('/usr/local/Caskroom/miniconda/base/envs/YOUR_ENVIRONMENT/lib/python3.10/site-packages/')
if package_path not in sys.path:
    sys.path.insert(0, package_path)

import numpy as np
from hstransform import HSTransform

# Create input signal (for example: Voltage signal)
t = np.linspace(0, 10, 100) # timeseries
V_m = 220*np.sqrt(2)  # peak voltage
f_V = 50  # frequency
phi_V = 0  # phase

V_clean = V_m * np.sin(2 * np.pi * f_V * t + phi_V)
# Create voltage sag/dip (80% of the nominal voltage for 0.15 second)
V_sag = np.where((t >= 2) & (t <= 3.5), 0.5 * V_clean, V_clean)

# Create an instance of HSTransform

hs = HSTransform()

# Perform the transform
signal = V_sag
S_transformed = hs.fit_transform(t, signal)

5.1 Power Quality Disturbance

Compare HS-transform vs. Morlet Wavelet Transform:

The figure showed HS-transform is able to detect the transient disturbances like notch, spike. Meanwhile, those signals from Morlet Wavelet transform are not obviously recognized.

We can see also different types of voltage disturbance can generate different real-imaginary trajectory in S-transform at different frequencies.

5.2 Power System Faults

As can be seen, both Wavelet and S-transform are able to detect when the fault occur (huge change in current magnitude). Wavelet transform seems more sensitive with noise with high distortion compared with HS-transform.

We can also observe different types of faults can generate different real-imaginary trajectory in S-transform at varying levels of frequencies.

6. Communication

If you have any questions, issues, or suggestions for HS Transform, please open an issue on the GitHub repository. or contact email: [email protected]

7. Citation

If you use HS Transform in your research, please cite it as follows: Linh V Nguyen (2024). HS Transform (Version 0.1) [Computer software]. GitHub: github.com/nvlinhvn/hstransform