Filtering in practice

Why this matters

L1.5 showed what a filter does to a signal. This lesson is about where the filter goes and which settings the analysis actually needs — because the same filter that is correct for an ICA fit will distort the ERP you are fitting it for, and the same filter applied to epochs instead of continuous data puts its edge artifacts inside your measurement window. Filtering is a pipeline decision before it is a signal-processing decision.

Concepts

Settings follow the goal, not the habit

There is no default filter that is right for everything, because the three things people do with EEG want different bands and tolerate different distortions.

ERPs. The components are slow and broad, so the high-pass is the dangerous filter. A conservative cutoff — on the order of 0.1 Hz or lower — preserves slow components such as P3 and the CNV; higher cutoffs attenuate them and, because offline filters are zero-phase, redistribute the removed energy symmetrically in time as artifactual opposite-polarity deflections before and after the real component (Tanner, 2015) . A low-pass in the region of 30 Hz is usually harmless for measurement and mostly cosmetic: it makes waveforms readable without changing a mean amplitude much. Report both cutoffs, the filter type, its length or order, and whether it was applied zero-phase (Widmann, 2015) .

Oscillations (Level 4). A higher high-pass — near 1 Hz — is common because drift otherwise dominates the low end of a spectrum, and the slow components an ERP analyst protects are not the object of study. The real hazard here is the opposite one: a narrow band-pass makes noise look rhythmic (L4.3, L4.6). Prefer estimating a spectrum on lightly filtered data.

An ICA fit. ICA is a stationary linear model, and slow drift is neither stationary nor low-dimensional. Fitting on data high-passed around 1 Hz gives markedly better-separated components than fitting on data high-passed at 0.1 Hz. But a 1 Hz high-pass is exactly what you must not apply to ERP data. That is the reason for the two-pass strategy.

The two-pass strategy

The key point is that ICA produces a matrix, not data. You can estimate the unmixing matrix on one version of the recording and apply it to another, as long as the two share the same channels in the same order and the same reference:

1. Copy the continuous data and high-pass the copy at about 1 Hz.
2. Fit ICA on the copy, with the correct rank (L2.2, L2.6).
3. Identify and mark the components to remove, using the copy.
4. Apply the resulting unmixing/mixing operation to the analysis data — the 0.1 Hz-filtered continuous recording — and reconstruct.

raw_analysis = raw.copy().filter(l_freq=0.1, h_freq=30.)     # what you will analyse
raw_for_ica  = raw.copy().filter(l_freq=1.0, h_freq=None)    # what ICA sees
ica = mne.preprocessing.ICA(n_components=rank, random_state=seed)
ica.fit(raw_for_ica)
ica.exclude = [...]                                          # decided in L2.6
raw_clean = ica.apply(raw_analysis.copy())

What travels between the two copies is the matrix; the filtered signal does not. This is also why the widget’s pipeline mode draws the two copies side by side: they are different data, and the arrow between them carries only the unmixing.

Filter continuous data, before epoching

A filter needs samples on both sides of every point it computes. At the beginning and end of the data those samples do not exist, and the implementation pads — with zeros, a reflection, or a constant — so the first and last stretch of output, roughly as long as the filter’s impulse response, is contaminated.

On a continuous recording those contaminated stretches are at the ends of the file, minutes away from anything you care about. On a 1-second epoch they are inside the epoch, and for a low high-pass the impulse response is longer than the epoch itself: there is nowhere for the edge artifact to go. Filtering epoched data is the pitfall pf-filter-epoched-data below. The rule: filter the continuous recording, then epoch, and keep epoch edges well away from any transient you care about.

Boundaries and discontinuities

The same argument applies wherever the continuous data is discontinuous: two files concatenated, a recording break, a segment removed. A filter run across such a joint rings on both sides of it (pf-filter-across-boundaries).

MNE handles this with BAD boundary annotations: mne.concatenate_raws inserts them, and raw.filter() respects them when filtering, so each contiguous span is filtered independently. Two habits keep it honest: never remove data by slicing and re-concatenating the array yourself (mark it bad instead, L2.5), and check that the boundary annotations survived every step of your pipeline — cropping, resampling and re-referencing all preserve them, but a round trip through a format that does not store annotations does not.

Downsampling: after the low-pass, and only for a reason

Downsampling without an anti-alias low-pass folds high-frequency content into your band (pf-aliasing-on-downsample, L1.1). MNE’s raw.resample() applies the anti-alias filter for you, but two subtleties matter in a pipeline:

• Resample before epoching, or use Epochs.resample, but do not resample events separately. Event sample indices are only valid at the rate they were built for. Resampling continuous data with its annotations attached keeps the timing (annotations are in seconds); resampling an array of event samples by hand introduces jitter of up to one sample at the new rate, which can be several milliseconds.
• Ask what you gain. Downsampling 1024 Hz ERP CORE data to 256 Hz makes ICA about four times faster and costs nothing above 128 Hz that an ERP analysis wanted. Downsampling to 100 Hz to save disk, and then wanting gamma, is not recoverable.

A related habit worth keeping: the low-pass you apply for anti-aliasing is a real filter with real side effects, so state it with the others rather than treating the resampling call as a formatting step.

The data behind this lesson

• The widget’s traces are the Level 1 set: four 10-second single-channel recordings and one 8-channel segment from ds-eegbci (160 Hz, no hardware filters) plus a line-noise trace from ds-iowapd (500 Hz). In pipeline mode the filtering is illustrative of placement; the ERP consequences are measured in the notebook on real ERP data.
• The notebook works on ds-erpcore P3 data: CC BY 4.0, open, per-subject downloadable, 30 EEG + 3 EOG channels, 1024 Hz, 60 Hz mains, no software filters. TODO(confirm): the author mirrors the ERP CORE entry into the catalog registry and signs off the dataset page (§10.11 item 8).

Explore

Three things to do here: apply the same high-pass to the continuous trace and to a short epoch cut from it, and compare the epoch edges; move the filter from before epoching to after and watch what happens inside the analysis window; then switch on the two-pass view and check that the 1 Hz copy and the 0.1 Hz copy are visibly different data while the arrow between them carries only the unmixing matrix.

Practice

The notebook measures ERP distortion across high-pass cutoffs on ds-erpcore and demonstrates a boundary artifact by concatenating two runs with and without boundary handling. Its final cell prints the measured amplitudes and the boundary ringing duration.

Exercises

Three analyses, three sets of settings. Pick the defensible option for each, then write the reasoning.