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"""
================================
Temporal whitening with AR model
================================
This script shows how to fit an AR model to data and use it
to temporally whiten the signals.
"""
# Authors: Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>
#
# License: BSD (3-clause)
print(__doc__)
import numpy as np
from scipy import signal
import matplotlib.pyplot as plt
import mne
from mne.time_frequency import ar_raw
from mne.datasets import sample
data_path = sample.data_path()
raw_fname = data_path + '/MEG/sample/sample_audvis_raw.fif'
proj_fname = data_path + '/MEG/sample/sample_audvis_ecg_proj.fif'
raw = mne.io.Raw(raw_fname)
proj = mne.read_proj(proj_fname)
raw.info['projs'] += proj
raw.info['bads'] = ['MEG 2443', 'EEG 053'] # mark bad channels
# Set up pick list: Gradiometers - bad channels
picks = mne.pick_types(raw.info, meg='grad', exclude='bads')
order = 5 # define model order
picks = picks[:5]
# Estimate AR models on raw data
coefs = ar_raw(raw, order=order, picks=picks, tmin=60, tmax=180)
mean_coefs = np.mean(coefs, axis=0) # mean model across channels
filt = np.r_[1, -mean_coefs] # filter coefficient
d, times = raw[0, 1e4:2e4] # look at one channel from now on
d = d.ravel() # make flat vector
innovation = signal.convolve(d, filt, 'valid')
d_ = signal.lfilter([1], filt, innovation) # regenerate the signal
d_ = np.r_[d_[0] * np.ones(order), d_] # dummy samples to keep signal length
###############################################################################
# Plot the different time series and PSDs
plt.close('all')
plt.figure()
plt.plot(d[:100], label='signal')
plt.plot(d_[:100], label='regenerated signal')
plt.legend()
plt.figure()
plt.psd(d, Fs=raw.info['sfreq'], NFFT=2048)
plt.psd(innovation, Fs=raw.info['sfreq'], NFFT=2048)
plt.psd(d_, Fs=raw.info['sfreq'], NFFT=2048, linestyle='--')
plt.legend(('Signal', 'Innovation', 'Regenerated signal'))
plt.show()
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