EMD

EMD: Empirical Mode Decomposition and Hilbert-Huang Spectral Analyses in Python - Published in JOSS (2021)

https://gitlab.com/emd-dev/emd

Scientific Fields

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Empirical Mode Decomposition in Python <a href="https://gitlab.com/ajquinn/emd/commits/master"><img alt="pipeline status" src="https://gitlab.com/ajquinn/emd/badges/master/pipeline.svg" /></a>

https://gitlab.com/emd-dev/emd/blob/master/

A python package for Empirical Mode Decomposition and related spectral analyses.

Please note that this project is in active development for the moment - the API may change relatively quickly between releases!

# Installation

You can install the latest stable release from the PyPI repository

```
pip install emd
```

or clone and install the source code.

```
git clone https://gitlab.com/emd-dev/emd.git
cd emd
pip install .
```

Requirements are specified in requirements.txt. Main functionality only depends
on numpy and scipy for computation and matplotlib for visualisation.

# Quick Start

Full documentation can be found at https://emd.readthedocs.org and development/issue tracking at gitlab.com/emd-dev/emd

Import emd

```python
import emd
```

Define a simulated waveform containing a non-linear wave at 5Hz and a sinusoid at 1Hz.

```python
sample_rate = 1000
seconds = 10
num_samples = sample_rate*seconds

import numpy as np
time_vect = np.linspace(0, seconds, num_samples)

freq = 5
nonlinearity_deg = .25  # change extent of deformation from sinusoidal shape [-1 to 1]
nonlinearity_phi = -np.pi/4  # change left-right skew of deformation [-pi to pi]
x = emd.simulate.abreu2010(freq, nonlinearity_deg, nonlinearity_phi, sample_rate, seconds)
x += np.cos(2*np.pi*1*time_vect)
```

Estimate IMFs

```python
imf = emd.sift.sift(x)
```

Compute instantaneous frequency, phase and amplitude using the Normalised Hilbert Transform Method.

```python
IP, IF, IA = emd.spectra.frequency_transform(imf, sample_rate, 'hilbert')
```
Compute Hilbert-Huang spectrum

```python
freq_range = (0, 10, 100)  # 0 to 10Hz in 100 steps
f, hht = emd.spectra.hilberthuang(IF, IA, freq_range, sum_time=False)
```
```
Make a summary plot

```python
import matplotlib.pyplot as plt
plt.figure(figsize=(16, 8))
plt.subplot(211, frameon=False)
plt.plot(time_vect, x, 'k')
plt.plot(time_vect, imf[:, 0]-4, 'r')
plt.plot(time_vect, imf[:, 1]-8, 'g')
plt.plot(time_vect, imf[:, 2]-12, 'b')
plt.xlim(time_vect[0], time_vect[-1])
plt.grid(True)
plt.subplot(212)
plt.pcolormesh(time_vect, f, hht, cmap='ocean_r')
plt.ylabel('Frequency (Hz)')
plt.xlabel('Time (secs)')
plt.grid(True)
plt.show()
```

JOSS Publication

EMD: Empirical Mode Decomposition and Hilbert-Huang Spectral Analyses in Python

Published

March 31, 2021

DOI

10.21105/joss.02977

Volume 6, Issue 59, Page 2977

Authors

Andrew J. Quinn
Oxford Centre for Human Brain Activity, Wellcome Centre for Integrative Neuroimaging, Department of Psychiatry, University of Oxford, Oxford, UK

Vitor Lopes-dos-Santos
Medical Research Council Brain Network Dynamics Unit, Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, OX1 3TH, United Kingdom

David Dupret
Medical Research Council Brain Network Dynamics Unit, Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, OX1 3TH, United Kingdom

Anna Christina Nobre
Oxford Centre for Human Brain Activity, Wellcome Centre for Integrative Neuroimaging, Department of Psychiatry, University of Oxford, Oxford, UK, Department of Experimental Psychology, University of Oxford, Oxford, OX2 6GG, UK

Mark W. Woolrich
Oxford Centre for Human Brain Activity, Wellcome Centre for Integrative Neuroimaging, Department of Psychiatry, University of Oxford, Oxford, UK

Editor

David P. Sanders

Tags

Time-series Non-linear Dynamics

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