Empirical Mode Decomposition

## Project description

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

```
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()
```

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