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

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/ajquinn/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

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.utils.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_stats( imf, sample_rate, 'nht' )

Compute Hilbert-Huang spectrum

freq_edges,freq_bins = emd.spectra.define_hist_bins(0,10,100)
hht = emd.spectra.hilberthuang( IF, IA, freq_edges )

Make a summary plot

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(2,1,2)
plt.pcolormesh( time_vect, freq_bins, hht, cmap='ocean_r' )
plt.ylabel('Frequency (Hz)')
plt.xlabel('Time (secs)')
plt.grid(True)
plt.show()