"""
==================================================
Compute the power spectral density of raw data
==================================================

This script shows how to compute the power spectral density (PSD)
of measurements on a raw dataset. It also show the effect of applying SSP
to the data to reduce ECG and EOG artifacts.
"""
# Authors: Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>
#          Martin Luessi <mluessi@nmr.mgh.harvard.edu>
#          Eric Larson <larson.eric.d@gmail.com>
# License: BSD (3-clause)

import numpy as np
import matplotlib.pyplot as plt

import mne
from mne import io, read_proj, read_selection
from mne.datasets import sample
from mne.time_frequency import psd_multitaper

print(__doc__)

###############################################################################
# Load data
# ---------
#
# We'll load a sample MEG dataset, along with SSP projections that will
# allow us to reduce EOG and ECG artifacts. For more information about
# reducing artifacts, see the preprocessing section in :ref:`documentation`.

data_path = sample.data_path()
raw_fname = data_path + '/MEG/sample/sample_audvis_raw.fif'
proj_fname = data_path + '/MEG/sample/sample_audvis_eog-proj.fif'

tmin, tmax = 0, 60  # use the first 60s of data

# Setup for reading the raw data (to save memory, crop before loading)
raw = io.read_raw_fif(raw_fname).crop(tmin, tmax).load_data()
raw.info['bads'] += ['MEG 2443', 'EEG 053']  # bads + 2 more

# Add SSP projection vectors to reduce EOG and ECG artifacts
projs = read_proj(proj_fname)
raw.add_proj(projs, remove_existing=True)


fmin, fmax = 2, 300  # look at frequencies between 2 and 300Hz
n_fft = 2048  # the FFT size (n_fft). Ideally a power of 2

###############################################################################
# Plot the raw PSD
# ----------------
#
# First we'll visualize the raw PSD of our data. We'll do this on all of the
# channels first. Note that there are several parameters to the
# :meth:`mne.io.Raw.plot_psd` method, some of which will be explained below.

raw.plot_psd(area_mode='range', tmax=10.0, show=False, average=True)

###############################################################################
# Plot a cleaned PSD
# ------------------
#
# Next we'll focus the visualization on a subset of channels.
# This can be useful for identifying particularly noisy channels or
# investigating how the power spectrum changes across channels.
#
# We'll visualize how this PSD changes after applying some standard
# filtering techniques. We'll first apply the SSP projections, which is
# accomplished with the ``proj=True`` kwarg. We'll then perform a notch filter
# to remove particular frequency bands.

# Pick MEG magnetometers in the Left-temporal region
selection = read_selection('Left-temporal')
picks = mne.pick_types(raw.info, meg='mag', eeg=False, eog=False,
                       stim=False, exclude='bads', selection=selection)

# Let's just look at the first few channels for demonstration purposes
picks = picks[:4]

plt.figure()
ax = plt.axes()
raw.plot_psd(tmin=tmin, tmax=tmax, fmin=fmin, fmax=fmax, n_fft=n_fft,
             n_jobs=1, proj=False, ax=ax, color=(0, 0, 1),  picks=picks,
             show=False, average=True)

raw.plot_psd(tmin=tmin, tmax=tmax, fmin=fmin, fmax=fmax, n_fft=n_fft,
             n_jobs=1, proj=True, ax=ax, color=(0, 1, 0), picks=picks,
             show=False, average=True)

# And now do the same with SSP + notch filtering
# Pick all channels for notch since the SSP projection mixes channels together
raw.notch_filter(np.arange(60, 241, 60), n_jobs=1, fir_design='firwin')
raw.plot_psd(tmin=tmin, tmax=tmax, fmin=fmin, fmax=fmax, n_fft=n_fft,
             n_jobs=1, proj=True, ax=ax, color=(1, 0, 0), picks=picks,
             show=False, average=True)

ax.set_title('Four left-temporal magnetometers')
plt.legend(ax.lines[::3], ['Without SSP', 'With SSP', 'SSP + Notch'])

###############################################################################
# Alternative functions for PSDs
# ------------------------------
#
# There are also several functions in MNE that create a PSD using a Raw
# object. These are in the :mod:`mne.time_frequency` module and begin with
# ``psd_*``. For example, we'll use a multitaper method to compute the PSD
# below.

f, ax = plt.subplots()
psds, freqs = psd_multitaper(raw, low_bias=True, tmin=tmin, tmax=tmax,
                             fmin=fmin, fmax=fmax, proj=True, picks=picks,
                             n_jobs=1)
psds = 10 * np.log10(psds)
psds_mean = psds.mean(0)
psds_std = psds.std(0)

ax.plot(freqs, psds_mean, color='k')
ax.fill_between(freqs, psds_mean - psds_std, psds_mean + psds_std,
                color='k', alpha=.5)
ax.set(title='Multitaper PSD', xlabel='Frequency',
       ylabel='Power Spectral Density (dB)')
plt.show()
