Implementation of the Empirical Mode Decomposition (EMD) and its variations

# PyEMD

## Introduction

This is yet another Python implementation of Empirical Mode Decomposition (EMD). The package contains many EMD variations and intends to deliver more in time.

### EMD variations:

• Ensemble EMD (EEMD),
• "Complete Ensemble EMD" (CEEMDAN)
• different settings and configurations of vanilla EMD.
• Image decomposition (EMD2D & BEMD) (experimental, no support)

PyEMD allows to use different splines for envelopes, stopping criteria and extrema interpolation.

### Available splines:

• Natural cubic [default]
• Pointwise cubic
• Akima
• Linear

### Available stopping criteria:

• Cauchy convergence [default]
• Fixed number of iterations
• Number of consecutive proto-imfs

### Extrema detection:

• Discrete extrema [default]
• Parabolic interpolation

## Installation

### Recommended

Simply download this directory either directly from GitHub, or using command line:

$git clone https://github.com/laszukdawid/PyEMD Then go into the downloaded project and run from command line:$ python setup.py install

### PyPi

Packaged obtained from PyPi is/will be slightly behind this project, so some features might not be the same. However, it seems to be the easiest/nicest way of installing any Python packages, so why not this one?

### EEMD

Simplest case of using Ensemble EMD (EEMD) is by importing EEMD and passing your signal to the instance or eemd() method.

Windows: Please don't skip the if __name__ == "__main__" section.

from PyEMD import EEMD
import numpy as np

if __name__ == "__main__":
s = np.random.random(100)
eemd = EEMD()
eIMFs = eemd(s)


### CEEMDAN

As with previous methods, there is also simple way to use CEEMDAN.

Windows: Please don't skip the if __name__ == "__main__" section.

from PyEMD import CEEMDAN
import numpy as np

if __name__ == "__main__":
s = np.random.random(100)
ceemdan = CEEMDAN()
cIMFs = ceemdan(s)


### Visualisation

The package contain a simple visualisation helper that can help, e.g., with time series and instantaneous frequencies.

import numpy as np
from PyEMD import EMD, Visualisation

t = np.arange(0, 3, 0.01)
S = np.sin(13*t + 0.2*t**1.4) - np.cos(3*t)

# Extract imfs and residue
# In case of EMD
emd = EMD()
emd.emd(S)
imfs, res = emd.get_imfs_and_residue()

# In general:
#components = EEMD()(S)
#imfs, res = components[:-1], components[-1]

vis = Visualisation()
vis.plot_imfs(imfs=imfs, residue=res, t=t, include_residue=True)
vis.plot_instant_freq(t, imfs=imfs)
vis.show()


### EMD2D/BEMD

Unfortunately, this is Experimental and we can't guarantee that the output is meaningful. The simplest use is to pass image as monochromatic numpy 2D array. Sample as with the other modules one can use the default setting of an instance or, more explicitly, use the emd2d() method.

from PyEMD.EMD2d import EMD2D  #, BEMD
import numpy as np

x, y = np.arange(128), np.arange(128).reshape((-1,1))
img = np.sin(0.1*x)*np.cos(0.2*y)
emd2d = EMD2D()  # BEMD() also works
IMFs_2D = emd2d(img)


## F.A.Q

### Why is EEMD/CEEMDAN so slow?

Unfortunately, that's their nature. They execute EMD multiple times every time with slightly modified version. Added noise can cause a creation of many extrema which will decrease performance of the natural cubic spline. For some tweaks on how to deal with that please see Speedup tricks in the documentation.

## Contact

Feel free to contact me with any questions, requests or simply to say hi. It's always nice to know that I've helped someone or made their work easier. Contributing to the project is also acceptable and warmly welcomed.

Contact me either through gmail (laszukdawid @ gmail) or search me through your favourite web search.

### Citation

If you found this package useful and would like to cite it in your work please use the following structure:

@misc{pyemd,
author = {Laszuk, Dawid},
title = {Python implementation of Empirical Mode Decomposition algorithm},
year = {2017},
publisher = {GitHub},
journal = {GitHub Repository},
howpublished = {\url{https://github.com/laszukdawid/PyEMD}},
}