Temporal whitening with AR model

Here we fit an AR model to the data and use it to temporally whiten the signals.

# Authors: Alexandre Gramfort <alexandre.gramfort@inria.fr>
#
# License: BSD-3-Clause
# Copyright the MNE-Python contributors.

import matplotlib.pyplot as plt
import numpy as np
from scipy import signal

import mne
from mne.datasets import sample
from mne.time_frequency import fit_iir_model_raw

print(__doc__)

data_path = sample.data_path()
meg_path = data_path / "MEG" / "sample"
raw_fname = meg_path / "sample_audvis_raw.fif"
proj_fname = meg_path / "sample_audvis_ecg-proj.fif"

raw = mne.io.read_raw_fif(raw_fname)
proj = mne.read_proj(proj_fname)
raw.add_proj(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[:1]

# Estimate AR models on raw data
b, a = fit_iir_model_raw(raw, order=order, picks=picks, tmin=60, tmax=180)
d, times = raw[0, 10000:20000]  # look at one channel from now on
d = d.ravel()  # make flat vector
innovation = signal.convolve(d, a, "valid")
d_ = signal.lfilter(b, a, 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()

Estimated memory usage: 0 MB