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%matplotlib inline

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.

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# Authors: Alexandre Gramfort <>
#          Martin Luessi <>
#          Eric Larson <>
# 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


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 documentation.

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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()['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 method, some of which will be explained below.

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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.

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# Pick MEG magnetometers in the Left-temporal region
selection = read_selection('Left-temporal')
picks = mne.pick_types(, 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]

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.

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f, ax = plt.subplots()
psds, freqs = psd_multitaper(raw, low_bias=True, tmin=tmin, tmax=tmax,
                             fmin=fmin, fmax=fmax, proj=True, picks=picks,
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)')