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!

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.

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

Import emd

import emd

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

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

imf = emd.sift.sift(x)

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

IP, IF, IA = emd.spectra.frequency_transform(imf, sample_rate, 'hilbert')

Compute Hilbert-Huang spectrum

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()