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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Temporal whitening with AR model
Here we fit an AR model to the data and use it
to temporally whiten the signals.
Step1:  Plot the different time series and PSDs
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Python Code:
# Authors: Alexandre Gramfort <alexandre.gramfort@inria.fr>
#
# License: BSD-3-Clause
import numpy as np
from scipy import signal
import matplotlib.pyplot as plt
import mne
from mne.time_frequency import fit_iir_model_raw
from mne.datasets import sample
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
Explanation: Temporal whitening with AR model
Here we fit an AR model to the data and use it
to temporally whiten the signals.
End of explanation
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()
Explanation: Plot the different time series and PSDs
End of explanation
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