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

Project description

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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)

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



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

$ git clone

Then go into the downloaded project and run from command line:

$ python install


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?

$ pip install EMD-signal


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


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: $S(t) = cos(22 \pi t^2) + 6t^2$



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

from PyEMD import EEMD
import numpy as np

s = np.random.random(100)
eemd = EEMD()
eIMFs = eemd(s)


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

from PyEMD import CEEMDAN
import numpy as np

s = np.random.random(100)
ceemdan = CEEMDAN()
cIMFs = ceemdan(s)


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()
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)


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 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)


Feel free to contact me with any questions, requests or simply to say hi. It's always nice to know that I one's work have eased others and saved someone's time. Contributing to the project is also acceptable.

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


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

Dawid Laszuk (2017-), Python implementation of Empirical Mode Decomposition algorithm.

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