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%matplotlib inline
This tutorial covers filtering and resampling, and gives examples of how filtering can be used for artifact repair. :depth: 2
We begin as always by importing the necessary Python modules and loading some
example data <sample-dataset>
. We'll also crop the data to 60 seconds
(to save memory on the documentation server):
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import os
import numpy as np
import matplotlib.pyplot as plt
import mne
sample_data_folder = mne.datasets.sample.data_path()
sample_data_raw_file = os.path.join(sample_data_folder, 'MEG', 'sample',
'sample_audvis_raw.fif')
raw = mne.io.read_raw_fif(sample_data_raw_file)
raw.crop(0, 60).load_data() # use just 60 seconds of data, to save memory
A filter removes or attenuates parts of a signal. Usually, filters act on
specific frequency ranges of a signal — for example, suppressing all
frequency components above or below a certain cutoff value. There are many
ways of designing digital filters; see disc-filtering
for a longer
discussion of the various approaches to filtering physiological signals in
MNE-Python.
Artifacts that are restricted to a narrow frequency range can sometimes be repaired by filtering the data. Two examples of frequency-restricted artifacts are slow drifts and power line noise. Here we illustrate how each of these can be repaired by filtering.
Low-frequency drifts in raw data can usually be spotted by plotting a fairly
long span of data with the :meth:~mne.io.Raw.plot
method, though it is
helpful to disable channel-wise DC shift correction to make slow drifts
more readily visible. Here we plot 60 seconds, showing all the magnetometer
channels:
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mag_channels = mne.pick_types(raw.info, meg='mag')
raw.plot(duration=60, order=mag_channels, proj=False,
n_channels=len(mag_channels), remove_dc=False)
A half-period of this slow drift appears to last around 10 seconds, so a full period would be 20 seconds, i.e., $\frac{1}{20} \mathrm{Hz}$. To be sure those components are excluded, we want our highpass to be higher than that, so let's try $\frac{1}{10} \mathrm{Hz}$ and $\frac{1}{5} \mathrm{Hz}$ filters to see which works best:
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for cutoff in (0.1, 0.2):
raw_highpass = raw.copy().filter(l_freq=cutoff, h_freq=None)
fig = raw_highpass.plot(duration=60, order=mag_channels, proj=False,
n_channels=len(mag_channels), remove_dc=False)
fig.subplots_adjust(top=0.9)
fig.suptitle('High-pass filtered at {} Hz'.format(cutoff), size='xx-large',
weight='bold')
Looks like 0.1 Hz was not quite high enough to fully remove the slow drifts. Notice that the text output summarizes the relevant characteristics of the filter that was created. If you want to visualize the filter, you can pass the same arguments used in the call to :meth:`raw.filter()
<mne.io.Raw.filter>above to the function :func:
mne.filter.create_filterto get the filter parameters, and then pass the filter parameters to
:func:
mne.viz.plot_filter. :func:
~mne.filter.create_filteralso requires
parameters ``data`` (a :class:
NumPy array <numpy.ndarray>) and ``sfreq``
(the sampling frequency of the data), so we'll extract those from our
:class:
~mne.io.Raw` object:
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filter_params = mne.filter.create_filter(raw.get_data(), raw.info['sfreq'],
l_freq=0.2, h_freq=None)
Notice that the output is the same as when we applied this filter to the data
using :meth:raw.filter() <mne.io.Raw.filter>
. You can now pass the filter
parameters (and the sampling frequency) to :func:~mne.viz.plot_filter
to
plot the filter:
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mne.viz.plot_filter(filter_params, raw.info['sfreq'], flim=(0.01, 5))
Power line noise is an environmental artifact that manifests as persistent
oscillations centered around the AC power line frequency
_. Power line
artifacts are easiest to see on plots of the spectrum, so we'll use
:meth:~mne.io.Raw.plot_psd
to illustrate. We'll also write a little
function that adds arrows to the spectrum plot to highlight the artifacts:
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def add_arrows(axes):
# add some arrows at 60 Hz and its harmonics
for ax in axes:
freqs = ax.lines[-1].get_xdata()
psds = ax.lines[-1].get_ydata()
for freq in (60, 120, 180, 240):
idx = np.searchsorted(freqs, freq)
# get ymax of a small region around the freq. of interest
y = psds[(idx - 4):(idx + 5)].max()
ax.arrow(x=freqs[idx], y=y + 18, dx=0, dy=-12, color='red',
width=0.1, head_width=3, length_includes_head=True)
fig = raw.plot_psd(fmax=250, average=True)
add_arrows(fig.axes[:2])
It should be evident that MEG channels are more susceptible to this kind of
interference than EEG that is recorded in the magnetically shielded room.
Removing power-line noise can be done with a notch filter,
applied directly to the :class:~mne.io.Raw
object, specifying an array of
frequencies to be attenuated. Since the EEG channels are relatively
unaffected by the power line noise, we'll also specify a picks
argument
so that only the magnetometers and gradiometers get filtered:
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meg_picks = mne.pick_types(raw.info, meg=True)
freqs = (60, 120, 180, 240)
raw_notch = raw.copy().notch_filter(freqs=freqs, picks=meg_picks)
for title, data in zip(['Un', 'Notch '], [raw, raw_notch]):
fig = data.plot_psd(fmax=250, average=True)
fig.subplots_adjust(top=0.85)
fig.suptitle('{}filtered'.format(title), size='xx-large', weight='bold')
add_arrows(fig.axes[:2])
:meth:~mne.io.Raw.notch_filter
also has parameters to control the notch
width, transition bandwidth and other aspects of the filter. See the
docstring for details.
EEG and MEG recordings are notable for their high temporal precision, and are often recorded with sampling rates around 1000 Hz or higher. This is good when precise timing of events is important to the experimental design or analysis plan, but also consumes more memory and computational resources when processing the data. In cases where high-frequency components of the signal are not of interest and precise timing is not needed (e.g., computing EOG or ECG projectors on a long recording), downsampling the signal can be a useful time-saver.
In MNE-Python, the resampling methods (:meth:`raw.resample()
<mne.io.Raw.resample>, :meth:
epochs.resample() <mne.Epochs.resample>and
:meth:
evoked.resample() <mne.Evoked.resample>) apply a low-pass filter to
the signal to avoid
aliasing_, so you don't need to explicitly filter it
yourself first. This built-in filtering that happens when using
:meth:
raw.resample() <mne.io.Raw.resample>, :meth:
epochs.resample()
<mne.Epochs.resample>, or :meth:
evoked.resample() <mne.Evoked.resample>is
a brick-wall filter applied in the frequency domain at the
Nyquist
frequency_ of the desired new sampling rate. This can be clearly seen in the
PSD plot, where a dashed vertical line indicates the filter cutoff; the
original data had an existing lowpass at around 172 Hz (see
``raw.info['lowpass']``), and the data resampled from 600 Hz to 200 Hz gets
automatically lowpass filtered at 100 Hz (the
Nyquist frequency`_ for a
target rate of 200 Hz):
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raw_downsampled = raw.copy().resample(sfreq=200)
for data, title in zip([raw, raw_downsampled], ['Original', 'Downsampled']):
fig = data.plot_psd(average=True)
fig.subplots_adjust(top=0.9)
fig.suptitle(title)
plt.setp(fig.axes, xlim=(0, 300))
Because resampling involves filtering, there are some pitfalls to resampling at different points in the analysis stream:
Performing resampling on :class:~mne.io.Raw
data (before epoching) will
negatively affect the temporal precision of Event arrays, by causing
jitter
_ in the event timing. This reduced temporal precision will
propagate to subsequent epoching operations.
Performing resampling after epoching can introduce edge artifacts on
every epoch, whereas filtering the :class:~mne.io.Raw
object will only
introduce artifacts at the start and end of the recording (which is often
far enough from the first and last epochs to have no affect on the
analysis).
The following section suggests best practices to mitigate both of these issues.
To avoid the reduction in temporal precision of events that comes with
resampling a :class:~mne.io.Raw
object, and also avoid the edge artifacts
that come with filtering an :class:~mne.Epochs
or :class:~mne.Evoked
object, the best practice is to:
low-pass filter the :class:~mne.io.Raw
data at or below
$\frac{1}{3}$ of the desired sample rate, then
decimate the data after epoching, by either passing the decim
parameter to the :class:~mne.Epochs
constructor, or using the
:meth:~mne.Epochs.decimate
method after the :class:~mne.Epochs
have
been created.
The recommendation for setting the low-pass corner frequency at
$\frac{1}{3}$ of the desired sample rate is a fairly safe rule of
thumb based on the default settings in :meth:`raw.filter()
Note that this method of manually filtering and decimating is exact only when the original sampling frequency is an integer multiple of the desired new sampling frequency. Since the sampling frequency of our example data is 600.614990234375 Hz, ending up with a specific sampling frequency like (say) 90 Hz will not be possible:
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current_sfreq = raw.info['sfreq']
desired_sfreq = 90 # Hz
decim = np.round(current_sfreq / desired_sfreq).astype(int)
obtained_sfreq = current_sfreq / decim
lowpass_freq = obtained_sfreq / 3.
raw_filtered = raw.copy().filter(l_freq=None, h_freq=lowpass_freq)
events = mne.find_events(raw_filtered)
epochs = mne.Epochs(raw_filtered, events, decim=decim)
print('desired sampling frequency was {} Hz; decim factor of {} yielded an '
'actual sampling frequency of {} Hz.'
.format(desired_sfreq, decim, epochs.info['sfreq']))
If for some reason you cannot follow the above-recommended best practices, you should at the very least either:
resample the data after epoching, and make your epochs long enough that edge effects from the filtering do not affect the temporal span of the epoch that you hope to analyze / interpret; or
perform resampling on the :class:~mne.io.Raw
object and its
corresponding Events array simultaneously so that they stay more or less
in synch. This can be done by passing the Events array as the
events
parameter to :meth:raw.resample() <mne.io.Raw.resample>
.
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