Empirical Mode Decomposition
Project description
emd Empirical Mode Decomposition
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()
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