PyEMD

Introduction

Python implementation of the Empirical Mode Decomposition (EMD). The package contains multiple 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)
Just-in-time compiled EMD (JitEMD)

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

Available splines

Natural cubic (default)
Pointwise cubic
Hermite cubic
Akima
PChip
Linear

Available stopping criteria

Cauchy convergence (default)
Fixed number of iterations
Number of consecutive proto-imfs

Extrema detection

Discrete extrema (default)
Parabolic interpolation

Installation

PyPi (recommended)

The quickest way to install package is through pip.

$ pip install EMD-signal

In this way you install the latest stable release of PyEMD hosted on PyPi

From source

In case, if you only want to use EMD and its variations, the best way to install PyEMD is through pip. However, if you want the latest version of PyEMD, anyhow you might want to download the code and build package yourself. The source is publicaly available and hosted on GitHub. To download the code you can either go to the source code page and click Code -> Download ZIP, or use git command line

$ git clone https://github.com/laszukdawid/PyEMD

Installing package from source is done using command line:

$ python3 -m pip install .

after entering the PyEM directory created by git.

A quicker way to install PyEMD from source is done using pip and git in the same command:

$ python3 -m pip install git+https://github.com/laszukdawid/PyEMD.git

Note, however, that this will install it in your current environment. If you are working on many projects, or sharing reources with others, we suggest using virtual environments. If you want to make your installation editable use the -e flag for pip

Example

More detailed examples are included in the documentation or in the PyEMD/examples.

EMD

In most cases default settings are enough. Simply import EMD and pass your signal to instance or to emd() method.

from PyEMD import EMD
import numpy as np

s = np.random.random(100)
emd = EMD()
IMFs = emd(s)

The Figure below was produced with input: $S(t) = cos(22 \pi t^2) + 6t^2$

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, also there is a 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 contains 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()

Experimental

JitEMD

Just-in-time (JIT) compiled EMD is a version of EMD which exceed on very large signals or reusing the same instance multiple times. It's strongly sugested to be used in Jupyter notebooks when experimenting by modifyig input rather than the method itself.

The problem with JIT is that the compilation happens on the first execution and it can be quite costly. With small signals, or performing decomposition just once, the extra time for compilation will be significantly larger than the decomposition, making it less performant.

Please see documentation for more information or examples for how to use the code. This is experimental as it's value is still questionable, and the author (me) isn't proficient in JIT optimization so mistakes could've been made.

Any feedback is welcomed. Happy to improve if there's intrest. Please open tickets with questions and suggestions.

To enable JIT in your PyEMD, please install with jit option, i.e.

$ pip install EMD-signal[jit]

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.

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}},
  doi = {10.5281/zenodo.5459184}
}

laszukdawid/PyEMD