Filtering and resampling data

This tutorial covers filtering and resampling, and gives examples of how filtering can be used for artifact repair.

We begin as always by importing the necessary Python modules and loading some example data. We’ll also crop the data to 60 seconds (to save memory on the documentation server):

# Authors: The MNE-Python contributors.
# License: BSD-3-Clause
# Copyright the MNE-Python contributors.

import os

import matplotlib.pyplot as plt
import numpy as np

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)
# use just 60 seconds of data and mag channels, to save memory
raw.crop(0, 60).pick(picks=["mag", "stim"]).load_data()

Opening raw data file /home/circleci/mne_data/MNE-sample-data/MEG/sample/sample_audvis_raw.fif...
    Read a total of 3 projection items:
        PCA-v1 (1 x 102)  idle
        PCA-v2 (1 x 102)  idle
        PCA-v3 (1 x 102)  idle
    Range : 25800 ... 192599 =     42.956 ...   320.670 secs
Ready.
Reading 0 ... 36037  =      0.000 ...    60.000 secs...

	General
	Filename(s)	sample_audvis_raw.fif
	MNE object type	Raw
	Measurement date	2002-12-03 at 19:01:10 UTC
	Participant	Unknown
	Experimenter	MEG
	Acquisition
	Duration	00:01:01 (HH:MM:SS)
	Sampling frequency	600.61 Hz
	Time points	36,038
	Channels
	Magnetometers	102
	Stimulus	9
	Head & sensor digitization	146 points
	Filters
	Highpass	0.10 Hz
	Lowpass	172.18 Hz
	Projections	PCA-v1 (off) PCA-v2 (off) PCA-v3 (off)

Background on filtering

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 Background information on filtering for a longer discussion of the various approaches to filtering physiological signals in MNE-Python.

Repairing artifacts by filtering

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.

Slow drifts

Low-frequency drifts in raw data can usually be spotted by plotting a fairly long span of data with the 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:

raw.plot(duration=60, proj=False, n_channels=len(raw.ch_names), 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:

for cutoff in (0.1, 0.2):
    raw_highpass = raw.copy().filter(l_freq=cutoff, h_freq=None)
    with mne.viz.use_browser_backend("matplotlib"):
        fig = raw_highpass.plot(
            duration=60, proj=False, n_channels=len(raw.ch_names), remove_dc=False
        )
    fig.subplots_adjust(top=0.9)
    fig.suptitle(f"High-pass filtered at {cutoff} Hz", size="xx-large", weight="bold")

• 
• 

Filtering raw data in 1 contiguous segment
Setting up high-pass filter at 0.1 Hz

FIR filter parameters
---------------------
Designing a one-pass, zero-phase, non-causal highpass filter:
- Windowed time-domain design (firwin) method
- Hamming window with 0.0194 passband ripple and 53 dB stopband attenuation
- Lower passband edge: 0.10
- Lower transition bandwidth: 0.10 Hz (-6 dB cutoff frequency: 0.05 Hz)
- Filter length: 19821 samples (33.001 s)

[Parallel(n_jobs=1)]: Done  17 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done  71 tasks      | elapsed:    0.3s
Using matplotlib as 2D backend.
Using qt as 2D backend.
Filtering raw data in 1 contiguous segment
Setting up high-pass filter at 0.2 Hz

FIR filter parameters
---------------------
Designing a one-pass, zero-phase, non-causal highpass filter:
- Windowed time-domain design (firwin) method
- Hamming window with 0.0194 passband ripple and 53 dB stopband attenuation
- Lower passband edge: 0.20
- Lower transition bandwidth: 0.20 Hz (-6 dB cutoff frequency: 0.10 Hz)
- Filter length: 9911 samples (16.501 s)

[Parallel(n_jobs=1)]: Done  17 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done  71 tasks      | elapsed:    0.2s
Using matplotlib as 2D backend.
Using qt as 2D backend.

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 raw.filter() above to the function mne.filter.create_filter() to get the filter parameters, and then pass the filter parameters to mne.viz.plot_filter(). create_filter() also requires parameters data (a NumPy array) and sfreq (the sampling frequency of the data), so we’ll extract those from our Raw object:

filter_params = mne.filter.create_filter(
    raw.get_data(), raw.info["sfreq"], l_freq=0.2, h_freq=None
)

Setting up high-pass filter at 0.2 Hz

FIR filter parameters
---------------------
Designing a one-pass, zero-phase, non-causal highpass filter:
- Windowed time-domain design (firwin) method
- Hamming window with 0.0194 passband ripple and 53 dB stopband attenuation
- Lower passband edge: 0.20
- Lower transition bandwidth: 0.20 Hz (-6 dB cutoff frequency: 0.10 Hz)
- Filter length: 9911 samples (16.501 s)

Notice that the output is the same as when we applied this filter to the data using raw.filter(). You can now pass the filter parameters (and the sampling frequency) to plot_filter() to plot the filter:

mne.viz.plot_filter(filter_params, raw.info["sfreq"], flim=(0.01, 5))

Power line noise

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 compute_psd() to get a Spectrum object, and use its plot() method to illustrate. We’ll also write a little function that adds arrows to the spectrum plot to highlight the artifacts:

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.compute_psd(fmax=250).plot(
    average=True, amplitude=False, picks="data", exclude="bads"
)
add_arrows(fig.axes[:2])

Effective window size : 3.410 (s)
Plotting power spectral density (dB=True).

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 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:

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.compute_psd(fmax=250).plot(
        average=True, amplitude=False, picks="data", exclude="bads"
    )
    fig.suptitle(f"{title}filtered", size="xx-large", weight="bold")
    add_arrows(fig.axes[:2])

• 
• 

Filtering raw data in 1 contiguous segment
Setting up band-stop filter

FIR filter parameters
---------------------
Designing a one-pass, zero-phase, non-causal bandstop filter:
- Windowed time-domain design (firwin) method
- Hamming window with 0.0194 passband ripple and 53 dB stopband attenuation
- Lower transition bandwidth: 0.50 Hz
- Upper transition bandwidth: 0.50 Hz
- Filter length: 3965 samples (6.602 s)

[Parallel(n_jobs=1)]: Done  17 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done  71 tasks      | elapsed:    0.1s
Effective window size : 3.410 (s)
Plotting power spectral density (dB=True).
Effective window size : 3.410 (s)
Plotting power spectral density (dB=True).

notch_filter() also has parameters to control the notch width, transition bandwidth and other aspects of the filter. See the docstring for details.

It’s also possible to try to use a spectrum fitting routine to notch filter. In principle it can automatically detect the frequencies to notch, but our implementation generally does not do so reliably, so we specify the frequencies to remove instead, and it does a good job of removing the line noise at those frequencies:

raw_notch_fit = raw.copy().notch_filter(
    freqs=freqs, picks=meg_picks, method="spectrum_fit", filter_length="10s"
)
for title, data in zip(["Un", "spectrum_fit "], [raw, raw_notch_fit]):
    fig = data.compute_psd(fmax=250).plot(
        average=True, amplitude=False, picks="data", exclude="bads"
    )
    fig.suptitle(f"{title}filtered", size="xx-large", weight="bold")
    add_arrows(fig.axes[:2])

• 
• 

Filtering raw data in 1 contiguous segment
Removed notch frequencies (Hz):
     60.00 : 1122 windows
    120.00 : 1122 windows
    180.00 : 1122 windows
    239.00 : 1122 windows
    240.00 : 1122 windows
    241.00 : 1122 windows
Effective window size : 3.410 (s)
Plotting power spectral density (dB=True).
Effective window size : 3.410 (s)
Plotting power spectral density (dB=True).

Resampling

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 (raw.resample(), epochs.resample() and 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 raw.resample(), epochs.resample(), or 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):

raw_downsampled = raw.copy().resample(sfreq=200)
# choose n_fft for Welch PSD to make frequency axes similar resolution
n_ffts = [4096, int(round(4096 * 200 / raw.info["sfreq"]))]
fig, axes = plt.subplots(2, 1, sharey=True, layout="constrained", figsize=(10, 6))
for ax, data, title, n_fft in zip(
    axes, [raw, raw_downsampled], ["Original", "Downsampled"], n_ffts
):
    fig = data.compute_psd(n_fft=n_fft).plot(
        average=True, amplitude=False, picks="data", exclude="bads", axes=ax
    )
    ax.set(title=title, xlim=(0, 300))

86 events found on stim channel STI 014
Event IDs: [ 1  2  3  4  5 32]
86 events found on stim channel STI 014
Event IDs: [ 1  2  3  4  5 32]
Effective window size : 6.820 (s)
Plotting power spectral density (dB=True).
Effective window size : 6.820 (s)
Plotting power spectral density (dB=True).

By default, MNE-Python resamples using method="fft", which performs FFT-based resampling via scipy.signal.resample(). While efficient and good for most biological signals, it has two main potential drawbacks:

1. It assumes periodicity of the signal. We try to overcome this with appropriate signal padding, but some signal leakage may still occur.

2. It treats the entire signal as a single block. This means that in general effects are not guaranteed to be localized in time, though in practice they often are.

Alternatively, resampling can be performed using method="polyphase" instead. This uses scipy.signal.resample_poly() under the hood, which in turn utilizes a three-step process to resample signals (see scipy.signal.upfirdn() for details). This process guarantees that each resampled output value is only affected by input values within a limited range. In other words, output values are guaranteed to be a result of a specific set of input values.

In general, using method="polyphase" can also be faster than method="fft" in cases where the desired sampling rate is an integer factor different from the input sampling rate. For example:

n_ffts = [4096, 2048]  # factor of 2 smaller n_fft
raw_downsampled_poly = raw.copy().resample(
    sfreq=raw.info["sfreq"] / 2.0,
    method="polyphase",
    verbose=True,
)
fig, axes = plt.subplots(2, 1, sharey=True, layout="constrained", figsize=(10, 6))
for ax, data, title, n_fft in zip(
    axes, [raw, raw_downsampled_poly], ["Original", "Downsampled (polyphase)"], n_ffts
):
    data.compute_psd(n_fft=n_fft).plot(
        average=True, amplitude=False, picks="data", exclude="bads", axes=ax
    )
    ax.set(title=title, xlim=(0, 300))

86 events found on stim channel STI 014
Event IDs: [ 1  2  3  4  5 32]
Polyphase resampling neighborhood: ±2 input samples
86 events found on stim channel STI 014
Event IDs: [ 1  2  3  4  5 32]
Effective window size : 6.820 (s)
Plotting power spectral density (dB=True).
Effective window size : 6.820 (s)
Plotting power spectral density (dB=True).

Because resampling involves filtering, there are some pitfalls to resampling at different points in the analysis stream:

• Performing resampling on 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 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.

Best practices

To avoid the reduction in temporal precision of events that comes with resampling a Raw object, and also avoid the edge artifacts that come with filtering an Epochs or Evoked object, the best practice is to:

1. low-pass filter the Raw data at or below \(\frac{1}{3}\) of the desired sample rate, then

2. decimate the data after epoching, by either passing the decim parameter to the Epochs constructor, or using the decimate() method after the Epochs have been created.

Warning

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 raw.filter() (which are different from the filter settings used inside the raw.resample() method). If you use a customized lowpass filter (specifically, if your transition bandwidth is wider than 0.5× the lowpass cutoff), downsampling to 3× the lowpass cutoff may still not be enough to avoid aliasing, and MNE-Python will not warn you about it (because the raw.info object only keeps track of the lowpass cutoff, not the transition bandwidth). Conversely, if you use a steeper filter, the warning may be too sensitive. If you are unsure, plot the PSD of your filtered data before decimating and ensure that there is no content in the frequencies above the Nyquist frequency of the sample rate you’ll end up with after decimation.

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:

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 / 3.0

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"]
    )
)

Filtering raw data in 1 contiguous segment
Setting up low-pass filter at 29 Hz

FIR filter parameters
---------------------
Designing a one-pass, zero-phase, non-causal lowpass filter:
- Windowed time-domain design (firwin) method
- Hamming window with 0.0194 passband ripple and 53 dB stopband attenuation
- Upper passband edge: 28.60 Hz
- Upper transition bandwidth: 7.15 Hz (-6 dB cutoff frequency: 32.18 Hz)
- Filter length: 279 samples (0.465 s)

[Parallel(n_jobs=1)]: Done  17 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done  71 tasks      | elapsed:    0.1s
86 events found on stim channel STI 014
Event IDs: [ 1  2  3  4  5 32]
Not setting metadata
86 matching events found
Setting baseline interval to [-0.19813025304873463, 0.0] s
Applying baseline correction (mode: mean)
Created an SSP operator (subspace dimension = 3)
3 projection items activated
desired sampling frequency was 90 Hz; decim factor of 7 yielded an actual sampling frequency of 85.80214146205357 Hz.

If for some reason you cannot follow the above-recommended best practices, you should at the very least either:

1. 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

2. perform resampling on the 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 raw.resample().