PyEMD:经验模式分解（EMD）方法的Python实现

[](https://codecov.io/gh/laszukdawid/PyEMD) [](https://travis-ci.org/laszukdawid/PyEMD) [](https://pyemd.readthedocs.io/) [](https://www.codacy.com/app/laszukdawid/PyEMD?utm_source=github.com&utm_medium=referral&utm_content=laszukdawid/PyEMD&utm_campaign=badger) [](https://ko-fi.com/A0A110NUD) # PyEMD ## Links - HTML documentation: <https://pyemd.readthedocs.org> - Issue tracker: <https://github.com/laszukdawid/pyemd/issues> - Source code repository: <https://github.com/laszukdawid/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? > \$ pip install EMD-signal ## Example More detailed examples are included in the [documentation](https://pyemd.readthedocs.io/en/latest/examples.html) or in the [PyEMD/examples](https://github.com/laszukdawid/PyEMD/tree/master/example). ### EMD In most cases default settings are enough. Simply import `EMD` and pass your signal to instance or to `emd()` method. ```python 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. ```python 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. ```python 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. ```python 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. ```python 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](https://pyemd.readthedocs.io/en/latest/speedup_eemd.html) 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}}, } ```