HHTpywrapper instantaneously tracks frequency and amplitude variations of a signal generated by non-stationary and nonlinear processes (e.g., quasi-periodic oscillations of astronomical objects). It uses Python as an interface to call the Hilbert–Huang Transform (HHT) MATLAB package. HHT is a time-frequency analysis method to adaptively decompose a signal into basis components at different timescales (i.e., the empirical mode decomposition), and then Hilbert transform these components into instantaneous phases, frequencies and amplitudes as functions of time (i.e., Hilbert spectral analysis). HHT has been successfully applied to analyzing X-ray quasi-periodic oscillations from the active galactic nucleus RE J1034+396 (Hu et al. 2014) and two black hole X-ray binaries, XTE J1550–564 (Su et al. 2015) and GX 339-4 (Su et al. 2017). HHTpywrapper provides examples of reproducing HHT analysis results in Su et al. (2015) and Su et al. (2017). This project is originated from the Astro Hack Week 2015.
- Linux or Windows operating system (The fast EEMD code in the HHT MATLAB package has not supported Mac yet)
- Python 3.x+
- MATLAB
- Numpy
- Scipy
- Astropy
- Matplotlib
- pymatbridge (A simple Python => MATLAB(R) interface and a matlab magic for ipython)
- pyunpack and patool (For extracting the .zip/.rar HHT MATLAB package files)
- UNZIP and UNRAR (sudo apt-get install unzip unrar)
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Clone this project from GitHub:
$ git clone https://github.com/HHTpy/HHTpywrapper.git -
In the project directory, install required packages:
$ pip install -r requirements.txt -
In the project directory, execute:
$ python setup.py install
- Example of reproducing HHT analysis results in Su et al. 2015
- Example of reproducing HHT analysis results in Su et al. 2017
- Example of characterizing intermittency of an intermittent, frequency varying oscillation (To be added)
After finishing the installation, you can see the below directory structure:
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/Your Python site-packages path/hhtpywrapper/ :
This is the root directory of the package, including the directory of HHT MATLAB package and the Python API for calling the MATLAB package (eemd.py and hsa.py).
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/Your Python site-packages path/hhtpywrapper/HHT_MATLAB_package/ :
This is the base directory of HHT MATLAB package. There are three subdirectories: EEMD, checkIMFs and HSA.
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/Your Python site-packages path/hhtpywrapper/HHT_MATLAB_package/EEMD/ :
This directory collects MATLAB M-files for decomposing a signal into basis components (intrinsic mode functions, IMFs) defined by the signal itself. This adaptive decomposition method is called empirical mode decomposition (EMD). The M-files accomplished the most recently developed modified version of EMD, fast complementary ensemble empirical mode decomposition (CEEMD). Reference:
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/Your Python site-packages path/hhtpywrapper/HHT_MATLAB_package/checkIMFs/ :
This directory collects MATLAB M-files for checking IMF properties, including significance, index of orthogonality, and excessive extrema value. Reference:
- The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
- A confidence limit for the Empirical Mode Decomposition and Hilbert Spectral Analysis
- A study of the characteristics of white noise using the empirical mode decomposition method
- Ensemble Empirical Mode Decomposition: a noise-assisted data analysis method
- On Intrinsic Mode Function
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/Your Python site-packages path/hhtpywrapper/HHT_MATLAB_package/HSA/ :
This directory collects MATLAB M-files for calculating instantaneous amplitudes, phases and frequencies of IMFs (that is, the Hilbert Spectral Analysis, HSA). Reference:
- PyHHT ; PyHHT’s documentation (by Jaidev Deshpande)
- pyeemd (by Perttu Luukko)
- Python implementation of EMD/EEMD (by Dawid Laszuk)
- Yi-Hao Su (yhsu@astro.ncu.edu.tw)
HHTpywrapper is my project during the Astro Hack Week 2015. It is currently in development phase. Welcome any contributions and feedbacks!